delivered the opinion of the court:
Following a jury trial in the circuit court of Cook County, defendant, Randy Banks, was convicted of the murder of 16-month-old Veronica Hurley. (Ill. Rev. Stat. 1985, ch. 38, par. 9 — 1(a)(1).) The jury found defendant eligible for the death penalty based upon the statutory aggravating factor of murder of an individual under 12 years of age that resulted from exceptionally brutal or heinous behavior indicative of wanton cruelty. (Ill. Rev. Stat. 1985, ch. 38, par. 9 — 1(b)(7).) The same jury then found insufficient mitigating factors to preclude the imposition of the death sentence. Accordingly, the trial judge sentenced defendant to death.
Defendant’s sentence has been stayed pending direct review by this court. (Ill. Const. 1970, art. VI, § 4(b); 134 Ill. 2d Rules 603, 609(a).) For the reasons that follow, we affirm defendant’s conviction and death sentence.
SUMMARY OF FACTS
The record reveals the following pertinent facts. From September through December of 1986, Elaine Hurley and her three children, Victoria, age 5, Victor, age 21/a, and the 16-month-old victim lived with defendant in a four-bedroom apartment in Chicago. Defendant is the biological father of Victoria and Victor; however, he was not the father of the victim. After Hurley moved into the apartment, she worked full time as a cashier at a fast-food restaurant to support the family, while defendant stayed home and watched the children.
*124Hurley’s testimony at trial established that the three children suffered from repeated acts of physical abuse and cruelty during the four-month period in which they lived with defendant. The children slept together in a very small bedroom with one window. The room contained only the following furnishings: a mattress, pillow, toilet-training chair, and crate. There were no toys or blankets. The victim generally wore only a thin tee-shirt and a diaper. Victoria and Victor were naked approximately 90% of the time despite Victoria’s continuous requests for clothes. Once it became dark outside, the children’s room also remained dark because defendant refused to allow any lights in that room.
The apartment was unheated except for a space heater located in the living room where defendant and Hurley slept. According to Hurley, the children’s room became so cold that you could see "the breath come out of your mouth.” During the times that Hurley slept with the children in the bedroom, she wore her coat because it was so cold. Nevertheless, defendant opened the window in the children’s room three or four times each week so that he could air the room out. Victoria testified that she would curl up with Victor and the victim so that they could try to stay warm.
Hurley testified that defendant determined when the children would be fed. Defendant told Hurley, "These are my kids; I know what I am doing.” Victoria and Victor were fed only lunch meat or peanut butter and jelly sandwiches approximately two or three times per week. When Victoria begged defendant for food or clothing, he would beat her with a belt. On the days when the children received nothing to eat, Hurley would attempt to sneak food to them. However, if defendant caught Hurley sneaking food to the children, he would beat her. Victoria testified that she would sneak into the kitchen to get food at night after defendant fell asleep, which she would share with Victor.
*125Hurley prepared Similac, an infant formula, for defendant to feed to the victim while she was at work. However, three or four times per week she would return from work and find most of the formula where she had left it and consequently fed the baby herself. The baby would "gobble” the formula, and when defendant saw this he would take the food from her, contending that the baby was "acting like an animal.”
According to Hurley, the children never left the apartment. The victim could crawl when she first moved into the apartment. However, as the victim’s strength decreased, she no longer crawled. The victim lay on a pillow on the floor of the bedroom. Victoria was only allowed to leave the bedroom if she had to go to the bathroom. Victor was allowed to leave the bedroom only once or twice during the four-month period. Defendant refused to allow Hurley to take any of the children to a doctor. When Hurley argued with defendant over this issue, he struck and threatened to kill her.
Defendant demanded that Hurley turn over her paycheck to him, as he controlled the family’s money. Hurley did not mention the physical abuse to anyone at work because she was afraid that defendant would kill her mother and the children. Each day defendant sent Hurley to purchase enough food for the family for that day; however, he ate most of the food himself. He hid the remainder of Hurley’s earnings in various places in the apartment.
Defendant forced Victor to sit on the toilet-training chair throughout the day and night. Defendant provided a crate for him to lay his head on when he slept on the chair at night. If Victor left the chair, defendant would whip him by holding him up by one arm and striking him with a belt. The diaper that Victor wore came off, and the belt hit his penis, which then started bleeding. Hurley described Victor’s penis and testicles as bleeding, *126filled with pus, and swollen. The average beating consisted of over 10 blows, and occurred weekly.
Victoria received beatings from defendant approximately three times per week. Defendant struck Victoria more than 10 times in each beating, using either a belt or a "stick,” which she described as a two-by-four board. He struck her arms, back, legs, and buttocks, sometimes over 20 times during the beating. Defendant once knocked Victoria unconscious for over 10 minutes.
Victoria testified that her mother never beat her during that time. Her mother tried to help the children, but defendant continually prevented Hurley from doing so. Victoria also testified that defendant once sat her in a hot skillet on the stove, and that she suffered severe burns because of that episode.
The incidents of abuse culminated on the evening of December 22, 1986. When Hurley returned home from work that night, the victim refused to eat, and was lying very still. She dressed the victim and took her to the University of Illinois Hospital. Before Hurley left for the hospital, defendant told her to tell the doctor that the victim had just stopped eating that day. He also told her that she should mention nothing of him and the other two children at home.
Dr. Kenneth Greer, the senior pediatric resident, examined the victim upon her admission into the hospital. He testified that the victim was extremely emaciated, and her body was frigid to the touch. The victim’s body temperature was so low that Dr. Greer was unable to obtain an accurate measurement; however, after 45 minutes in the hospital, the victim’s body temperature rose to 78 degrees. She registered no blood pressure, and Dr. Greer could detect only faint and distant heart tones. The victim’s arms and legs had no fat, and her hands and feet were swollen, a sign of severe malnutrition. According to Dr. Greer, her skin *127showed signs of severe dehydration and lack of protein and adequate oxygen, similar to an individual who has suffered from starvation over an extended period.
Dr. Greer also testified that the victim had an extremely low white blood cell count, and suffered from a rampant blood infection. As a result, she was in a state of dissimulated intravascular coagulopathy, and was unable to form blood clots. She was so dehydrated that her blood vessels, which contained no significant amount of fluid, had collapsed. The victim also suffered from pressure sores on her back.
Dr. Greer’s attempt to save the victim’s life was ultimately unsuccessful. The victim died six hours after her arrival in the emergency room. The immediate cause of death was a pulmonary hemorrhage in her lungs due to the severe malnutrition and profound hypothermia. Dr. Greer testified that the profound hypothermia was consistent with the child’s having been kept in a room with the window open when the outside temperature was between 20 and 40 degrees for several days. The victim’s malnutrition was the result of not being fed, or being fed very little, over a long period.
Dr. Robert Stein, the chief medical examiner of Cook County, performed the autopsy on the victim. The 16-month-old victim weighed 17 pounds. Dr. Stein found that the victim was markedly emaciated and dehydrated, as evidenced by the edemal swelling of the upper and lower eyelids, and her large head size. He also found healed scars on the back of her leg, and an ulcerated area on her back. Dr. Stein found a complete absence of fat, which was consistent with starvation. The victim’s ribs were very prominent. There was a complete absence of food in her gastrointestinal tract, which showed that she had not eaten for days, possibly even a week. He found a localized hemorrhage in the subgaleal tissue on the victim’s head. Dr. Stein testified that the immediate *128cause of death was hypothermia due to neglect, because of child abuse.
After examination of the victim, the hospital authorities became concerned that other children might still be in the home subject to the same type of abuse that caused the victim’s death. Hurley told the hospital authorities that Victoria and Victor were still at home. The evidence established, however, that after Hurley took the victim to the hospital, defendant brought the other children to the home of his cousin, Theresa Robinson. Robinson testified that around midnight on the night of December 22, 1986, defendant arrived at her home accompanied by Victoria and Victor. Despite the winter’s cold, defendant was sweating profusely. Both children were terrified and in a great deal of pain. Victoria was barefoot, and wore no coat. Victor wore a coat and shoes that were too small. Defendant asked Robinson if she would care for the children for a few days. At first Robinson declined because it was so close to the Christmas holiday, but when she saw that Victoria was limping and in pain, she changed her mind. She told defendant that the children could stay for a short time, but that he had to return for them.
While Robinson prepared something for the children to eat, her daughter prepared a bath for them. After Victoria was undressed, Robinson observed scars, fresh wounds, and burns on her legs and buttocks. Robinson notified the police, and the children were immediately taken by the Chicago police department to Cook County Hospital.
The following day, around 3 p.m., defendant returned to Robinson’s home carrying a gym bag. Robinson and her husband explained to defendant that they had taken the children to the hospital. Defendant denied that he had harmed the children, and further stated that he did not care what happened to them because *129they were not his children. As defendant rose to leave Robinson’s house, Robinson’s husband told defendant that he "wasn’t going anywhere.” Robinson called the police, and defendant was placed under arrest. The arresting officer testified that the gym bag contained $4,427 in currency, neatly stacked in order of denomination and by the serial numbers on the bills.
Dr. Demetra Soter, the acting head of the child abuse team at Cook County Hospital, testified as to Victoria’s and Victor’s physical conditions upon their admission to the hospital. She described them as "emaciated, frightened children.” Victor did not speak at all. Dr. Soter observed lined and curved marks from a whip on Victor’s legs. Both of Victor’s feet were swollen and peeling from frostbite. Dr. Soter opined that the frostbite to Victor’s feet was consistent with his being kept in an unheated room, on a bare floor, during the month of December in Chicago. In addition, Victor had cuts all over his genitals and penis. Dr. Soter also observed a cigarette-type burn next to his rectum. Victor’s buttocks were very red and scarred, consistent with being placed on an object for a prolonged period. Dr. Soter diagnosed Victor as suffering from repeated severe child abuse and malnutrition.
According to Dr. Soter, Victoria was incredibly emaciated, with a very protuberant belly consistent with long-term starvation. Dr. Soter found cuts and bruises over Victoria’s head, and whip marks up and down her legs that were even more severe than those found on Victor’s legs. Similar to Victor, she had swollen hands and feet from frostbite. She had prominent scarring on her buttocks, and keloid formation, which she described as a permanent deformation caused by second- and third-degree burns. Victoria also had fresh bruises near her eyes and on her face. In addition, Dr. Soter noted linear marks on her hands and arms that could have *130been caused by being whipped with an extension cord with a tremendous amount of force. She diagnosed Victoria’s condition as severe starvation and abuse with burns and whips.
Chicago Police Detective Dennis Keane and his partner were assigned to investigate the victim’s death. The officers conducted three interviews with Hurley. She explained that during the first two interviews, she did not incriminate defendant because she was afraid of him. After learning during the third interview that defendant was in custody, however, she told the officers the complete truth because he was locked up and could not harm her.
The State then rested its case, and defendant, acting pro se, presented his case in chief. Defendant recalled Theresa Robinson to the stand, where she admitted that she had been convicted for possession of marijuana and possession of a pistol that was not registered. The defendant also recalled Hurley to the stand. Hurley denied that she made a deal with the State’s Attorney’s office whereby she would testify at trial so that she could gain custody of Victoria and Victor.
At the close of the evidence and arguments, the jury returned a verdict finding defendant guilty of murder. The same jury found that defendant was eligible for the death penalty based upon the statutory aggravating factor of murder of an individual under 12 years of age that resulted from exceptionally brutal or heinous behavior indicative of wanton cruelty. Ill. Rev. Stat. 1985, ch. 38, par. 9 — 1(b).
At the sentencing hearing, the State introduced evidence concerning defendant’s participation in a kidnap-ing and armed robbery that occurred on October 5, 1983, in Indianapolis, Indiana. On that date, the victim, Mrs. Hutchins, was at a motel in Indianapolis with her husband, who was attending a convention. Mrs. *131Hutchins met her husband at the entrance of the motel, and offered to get their car that was parked about 12 car lengths away from the door. As she attempted to unlock the car, she was accosted at gunpoint by two men and one woman. The offenders entered her car and forced her into the front seat. After driving around for approximately five minutes, she was ordered to remove her jewelry, cash, and clothing. She was sexually molested by one of the men. The car stopped near a remote field, and Hutchins was ordered to leave the car. The offenders tied her up and threatened her life at gunpoint. The three offenders left her naked and tied up in the field as they drove away in her car. Mrs. Hutchins was able to get up and hop, while she was still tied up, to a nearby apartment complex for help.
Officer Casey Forestal of the Marion County, Indiana, sheriff’s police testified that he was working as a security guard at a convenience store that same evening. He heard a sheriff’s radio broadcast concerning the kidnaping of Hutchins and a description of the car taken by the three offenders. Sometime later the same car pulled into the parking lot where he worked. As the vehicle backed out of its parking place, Officer Forestal drew his weapon, announced his office, and told the driver to stop and turn off the car. As Forestal radioed for assistance, defendant restarted the car and sped off. Forestal fired a flurry of shots, wounding the female accomplice. The female accomplice and the male offender were arrested within a short time. Defendant escaped, however, and was not taken into custody until he was arrested in Chicago four years later for the aggravated battery of Victoria and Victor. At defendant’s trial for these charges, Forestal positively identified defendant, then known as Waldo Short, as the driver' of the car. Defendant was convicted of kidnaping, armed robbery, possession of sawed-off shotguns, and resisting law *132enforcement officers, for which he was sentenced to 75 years in prison. Certified copies of these convictions, and two other theft convictions that occurred in 1981 and 1982, were introduced as evidence in aggravation.
Defendant did not present any mitigating evidence, and declined to make an opening or closing argument. The jury found no mitigating evidence sufficient to preclude the imposition of a death sentence. Accordingly, the judge sentenced defendant to death for the murder of the 16-month-old victim.
TRIAL ISSUES
A
Defendant first argues that he was not proven guilty of murder beyond a reasonable doubt because the State failed to establish that defendant was under a legal duty to provide the victim with food, clothing and adequate shelter or other necessities. At trial, defendant maintained that Hurley alone should have been legally accountable for the death of the victim. Defendant points out that he was not the natural father of the victim, and was never married to Hurley, the victim’s mother. He argues, therefore, that he lacked the parental status that would have imposed a legal duty upon him to safeguard and protect the victim.
Defendant asserts that the indictment charged him with killing the victim by physically neglecting her. He interprets the indictment as charging him with causing the victim’s death by failure to act in a particular manner. Defendant concedes that criminal conduct may arise from a failure to act or an omission. (People v. Stanciel (1992), 153 Ill. 2d 218, 236; Ill. Rev. Stat. 1985, ch. 38, par. 4 — 1.) Defendant argues, however, that an omission is criminal only when the defendant is under a legal duty to act.' He claims that the State did not prove that he was under a legal duty to protect the victim. He *133argues, therefore, that the State did not prove a material element of the offense, and that his murder conviction must be reversed.
However, we do not read the indictment as merely charging defendant with an omission or failure to act. The indictment charged that defendant "intentionally and knowingly killed [the victim] by physically neglecting her, depriving her of food, clothing, shelter, medical care, keeping her in a cold room and exposing her to the inclemency of the weather.” (Ill. Rev. Stat. 1985, ch. 38, par. 9 — 1(a)(1).) At trial, the State did not attempt to prove that the defendant failed to protect the victim from harm, as the defendant claims. Rather, the State advanced the theory that defendant deliberately committed various overt acts designed to cause the victim’s death.
Consistent with this theory, the State produced ample evidence at trial to show that defendant’s actions alone caused the victim’s death by starvation and profound hypothermia. For example, Hurley testified that she prepared infant formula for the victim before she left for work. However, when she returned home from work, she saw that defendant had only given a small portion of the food to the victim. When Hurley then attempted to feed the victim, defendant snatched the bottle away from Hurley because the victim was acting "like an animal.” Defendant controlled the amount of formula that the victim received, and chose to feed her only meager portions. Snatching the bottle from the infant’s mouth, and preventing Hurley from feeding the victim over an extended period, were overt acts that led to the starvation and eventual death of the victim.
Hurley’s testimony that the defendant prevented the victim from receiving adequate nourishment was corroborated by the condition of the victim’s body at the *134time of her death. Dr. Greer testified that the victim’s arms and legs had no fat, and her hands and feet were swollen, which is a sign of severe malnutrition. Defendant’s intentional attempt to starve the child to death is also evident from the evidence produced by the autopsy, which showed the complete absence of food in her gastrointestinal tract, and her emaciated and dehydrated condition.
Similarly, the record reveals that defendant embarked upon a deliberate course of conduct that caused the victim’s profound hypothermia. Hurley testified that the victim generally wore only a diaper and a thin tee-shirt. Prior to moving into the apartment, the victim was an active baby, able to crawl and propel herself across the room. However, as time progressed, the victim could only lie on the pillow on the floor. Defendant kept the bedroom door closed in the unheated room where the victim was forced to spend all of her time, thereby preventing the heat that emanated from the space heater in the living room from entering that room. In addition, defendant opened the window in the bedroom approximately 14 to 18 inches, four to six hours at a time, several times each week during the winter months of November and December, purportedly to "air the room out.”
Dr. Greer testified that when the child was brought into the emergency room, her body temperature was too low to be recorded on hospital equipment. According to Dr. Stein, the immediate cause of death was hypothermia due to child abuse. Victoria and Victor also suffered from frostbite on their feet and hands caused by prolonged exposure to the cold temperatures in the bedroom. The evidence clearly establishes, therefore, that defendant intentionally exposed the victim to subfreezing temperatures without the benefit of clothing or blankets. The defendant’s overt acts ultimately caused the victim’s death.
*135Most importantly, the State established that defendant intentionally prevented Hurley from coming to the aid of her children. When defendant caught Hurley trying to sneak food to her children, or to provide covers to protect the children from the inclemency of the weather, defendant beat and threatened to kill her. Hurley further testified that in early December, when the victim stopped moving, defendant hit her and threatened to kill her when she tried to take the victim to the doctor.
The record also reveals that the jury was instructed according to the theory propounded by the State, namely, that defendant’s overt acts caused the death of the victim. The instruction submitted to the jury stated that, in order to sustain the charge of murder, the State must prove that the defendant performed the acts that caused the death of the victim; that defendant intended to kill or do great bodily harm to the victim; or that he knew that his act would cause death or great bodily harm to the victim; or that his acts created a strong probability of death or great bodily harm to the victim. Illinois Pattern Jury Instructions, Criminal, No. 7.02 (2d ed. 1981).
This court has long held that it is the jury’s function to determine the accused’s guilt or innocence; "we will not reverse a conviction unless the evidence is so improbable as to justify a reasonable doubt of the accused’s guilt. [Citations.]” (People v. McDonald (1975), 62 Ill. 2d 448, 456.) When faced with a challenge to the sufficiency of the evidence against the accused, it is not the function of this court to retry the defendant. (People v. Collins (1985), 106 Ill. 2d 237, 261.) Rather, as the United States Supreme Court noted in Jackson v. Virginia (1979), 443 U.S. 307, 61 L. Ed. 2d 560, 99 S. Ct. 2781, "the relevant question is whether, after viewing the evidence in the light most favorable to the prosecution, any *136rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.” (Emphasis in original.) Jackson, 443 U.S. at 319, 61 L. Ed. 2d at 573, 99 S. Ct. at 2789.
Given all of the evidence adduced at trial, and reviewing it in the light most favorable to the prosecution, we conclude that any rational trier of fact could have found defendant guilty of murder beyond a reasonable doubt based upon the overt acts perpetrated by defendant against the victim.
In sum, the evidence presented at trial showed that defendant’s murder conviction rested upon his overt acts, rather than his failure to act in conformance with a legal duty of care. Consequently, we reject defendant’s contention that the State was obligated to introduce evidence relating to defendant’s legal duty.
B
Defendant next asserts that the trial court committed reversible error when it permitted the introduction of other-crimes evidence concerning the severe abuse defendant perpetrated against Victoria and Victor. Over defendant’s objection, the trial court granted the State’s pretrial motion to introduce such evidence on the theory that the abuse showed defendant’s motive, intent, modus operandi, common scheme, design, and absence of mistake or accident. Defendant argues that the other-crimes evidence was not supported by any of the aforementioned theories, and could not have been considered by the jury for any legitimate purpose. According to defendant, the admission of such conduct, for which he had not been charged, served only to suggest to the jury that it should hold defendant responsible for the victim’s death because of his violent nature and lack of moral character.
It is well established that evidence of collateral crimes is inadmissible if relevant only to establish the *137defendant’s propensity to commit crimes. (People v. Carlson (1982), 92 Ill. 2d 440; People v. Lindgren (1980), 79 Ill. 2d 129, 137; People v. Romero (1977), 66 Ill. 2d 325, 330.) However, evidence of other crimes committed by the accused may be admitted if it is probative of motive, intent, identity, absence of mistake or accident, the existence of a common design or plan, or modus operandi. (People v. Jones (1993), 156 Ill. 2d 225; People v. Lehman (1955), 5 Ill. 2d 337, 342-43.) "[I]t has been broadly held that evidence of other offenses is admissible if relevant for any purpose other than to show propensity to commit a crime.” People v. McDonald (1975), 62 Ill. 2d 448, 455.
In order for evidence of another crime to be admissible to establish design or plan, the two offenses must be so similar that evidence of the other crime tends to prove the defendant guilty of the offense charged. (People v. McKibbins (1983), 96 Ill. 2d 176, 185.) In the case sub judice, the crimes committed against Victoria and Victor occurred during the same period in which they shared the small unheated bedroom with the victim. Defendant subjected all three children to the same types of abuse, namely, starvation, exposure to subfreezing conditions, and deprivation of medical care. Distinct similarities existed between the victim’s death and the abuse suffered by Victoria and Victor. Dr. Greer testified that the victim’s death was a result of severe malnutrition and profound hypothermia. Likewise, the testimony of Dr. Soter established that when Victoria and Victor were first admitted to the hospital, they were emaciated and suffering from starvation. Victoria and Victor also suffered from frostbite on their hands and feet because of exposure to the subfreezing temperatures that defendant created by opening the window in the unheated room. As established by Dr. Soter’s testimony, the frostbite to Victor’s and Victoria’s feet was consistent *138with being kept in an unheated room, on a bare floor, during December in Chicago.
While the victim was not subjected to beatings as frequently as the other children, Victoria testified that the beatings were administered in response to her requests for food, clothing, or cover. The deprivation of these basic life necessities ultimately caused the death of the victim. Under the unique circumstances present in this case, it would be difficult to explain or describe the facts surrounding the victim’s death without introducing a substantial amount of evidence concerning the abuse simultaneously sustained by Victoria and Victor.
We also note that the jury was instructed that the evidence of the other crimes committed against Victoria and Victor was received solely on the issue of defendant’s presence, intent, motive, and design, and not to show a propensity on his part toward criminal conduct. Illinois Pattern Jury Instructions, Criminal, No. 3.14 (2d ed. 1981).
Accordingly, we find that the admission of the other-crimes evidence was relevant to show defendant’s motive, intent, and absence of mistake or accident in the manner in which he acted toward all three children that eventually caused the death of the victim.
C
Defendant further asserts that he was denied his right of self-representation pursuant to the sixth amendment. Defendant alleges that he was allowed access to the jail law library for only one hour on the day prior to court appearances. He argues, therefore, that he was unable to exercise his right of self-representation in a meaningful manner because he had only limited access to the law library and legal materials.
The record shows that defendant was arraigned on *139June 28, 1988. One month later, defendant informed the court that he wished to exercise his right to appear pro se. The trial judge found that defendant was capable of acting as his own counsel; nevertheless, he strongly admonished him against proceeding in that manner. Despite the trial judge’s repeated offers to appoint counsel to assist him from the public defender’s office, defendant persistently stated that he wished to represent himself throughout discovery, pretrial motions, and eventually at trial.
On August 15, 1988, defendant began to complain of inadequate access to the jail law library. The trial judge accommodated defendant’s request for additional library time, and ordered that defendant be allowed to use the law library four hours each week. Defendant continued to sound complaints that the correctional officers refused to comply with the judge’s order for additional library time. The trial judge granted defendant a continuance after each complaint, rather than forcing him to proceed while unprepared. After November 9, 1989, however, defendant made no further complaints, except to explain once that he was filing a handwritten rather than typed motion because he was unable to use the law library.
Defendant relies upon the United States Supreme Court holdings in Faretta v. California (1975), 422 U.S. 806,45 L. Ed. 2d 562, 95 S. Ct. 2525, and Bounds v. Smith (1977), 430 U.S. 817, 52 L. Ed. 2d 72, 97 S. Ct. 1491, as support for his claim that self-representation and meaningful access to the courts are among his constitutional rights. Defendant correctly notes that in Faretta, the Court recognized a sixth amendment “right of self-representation” which allows a defendant to refuse the assistance of trained counsel and conduct his own defense. (Faretta, 422 U.S. at 832, 45 L. Ed. 2d at 580, 95 S. Ct. at 2539.) In Bounds, the Court held that the fundamental constitutional right of access to the courts *140requires prison authorities to assist inmates in the preparation and filing of meaningful legal papers by providing prisoners with adequate law libraries or adequate assistance from persons trained in the law. Bounds, 430 U.S. at 828, 52 L. Ed. 2d at 83, 97 S. Ct. at 1498.
This court has never addressed the issue of whether a prisoner should be afforded unlimited access to a law library. However, decisions rendered in other jurisdictions have refused to read Bounds to require prison officials to grant prisoners unlimited access to law libraries simply because a prisoner has elected to appear pro se. For instance, in United States ex rel. George v. Lane (7th Cir. 1983), 718 F.2d 226, the Seventh Circuit held that a prisoner has no constitutional right to be provided access to a law library simply because he chose to refuse the services of court-appointed counsel. The court likewise held that a defendant does not have a "constitutional right to access to a computerized legal research system, paralegal training or a full-fledged law school education.” Lane, 718 F.2d at 232.
In Martin v. Davies (7th Cir. 1990), 917 F.2d 336, the Seventh Circuit again reaffirmed its position that a defendant is not entitled to limitless access to the law library simply because he has refused appointed counsel. In Martin, the court ultimately rejected the defendant’s claim for insufficient access to the law library because he failed to allege specific facts in support of his allegations. The court noted that defendant’s motion did not allege that he had missed court dates, was unable to make timely filings, was denied legal assistance to which he was entitled, or that he lost a case which could have been won. Martin, 917 F.2d at 340, citing Bruscino v. Carlson (7th Cir. 1988), 854 F.2d 162, 167. See also Lyons v. Powell (1st Cir. 1988), 838 F.2d 28 (pretrial detainee was not denied access to court by prison restrictions, since he was not constitutionally entitled to *141assistance of persons trained in law, and where authorities allowed periodic access to law facilities); People v. Uppole (1992), 228 Ill. App. 3d 281 (pretrial detainee failed to state claim for denial of access to courts in form of .pretrial limitations on access to legal materials, where detainee had copy of the Criminal Code of 1961 and pertinent supreme court rules, and the court repeatedly advised defendant of the seriousness of the offense and that standby counsel had been appointed to be ready to conduct defendant’s defense at any time); People v. Partee (1987), 157 Ill. App. 3d 231 (pretrial detainee was allowed adequate access to law library facilities where court ordered access through prosecutor’s law library, which was later rescinded because of defendant’s abuse of privilege, and where court ordered liberal access to county jail law library on defendant’s request).
We find it significant that defendant did not voice any complaints of inadequate access to the law library for over 20 months prior to trial. Defendant asserts that he was reluctant to complain because he believed that further protestations would be futile. We find defendant’s argument unavailing, for we note that at least on the occasions when defendant did complain of inadequate access to the law library, the trial judge always granted defendant a continuance so that he could adequately prepare his case. Defendant does not cite a single issue that he was forced to argue without proper time for preparation.
The constitutional right of access to the courts requires prison authorities to assist inmates by providing adequate law libraries or assistance from persons trained in the law. (Bounds, 430 U.S. at 828, 52 L. Ed. 2d at 83, 97 S. Ct. at 1498.) However, defendant has failed to make any specific allegations of fact to show that he was prejudiced by the prison authorities’ *142purported denial of adequate access to the law library. During the three-year pendency of this trial, defendant filed approximately 18 documents with various courts, including the trial court, the Federal district court, and this court. Given the overwhelming evidence presented by the State at trial, defendant’s assertion that increased access to the law library would have led to a different result, without further support, is meritless.
Moreover, the record demonstrates that defendant was repeatedly offered the assistance of persons trained in the law. On numerous occasions, the trial judge offered the assistance of counsel from the public defender’s office to aid defendant in his preparation of the case. The trial judge pointed out difficulties that arose to defendant’s detriment because of his continued self-representation in this capital case. Nonetheless, defendant adamantly refused all offers of assistance and insisted upon acting as his own counsel. The record reveals that defendant steadfastly refused to cooperate with any representative from the public defender’s office.
While it is true that defendant is entitled to the use of an adequate law library to prepare his defense (Bounds, 430 U.S. at 828, 52 L. Ed. 2d at 83, 97 S. Ct. at 1498), such a right is not without limitations. Defendant has failed to establish that he was denied adequate access to the law library. We therefore dismiss defendant’s argument that he was denied his sixth amendment right of self-representation.
D
Defendant also contends that he was denied a fair trial by certain remarks made by the prosecutor in the opening and closing statements. Specifically, defendant contends that: (1) the prosecutor made improper remarks about defendant’s attire that were designed to appeal to the racial and religious prejudices of the jurors, and (2) *143the prosecutor improperly suggested that defendant planned to murder Victoria and Victor to eliminate them as witnesses to the charged offenses.
Defendant failed to object to these comments at trial and did not include this alleged error in his post-trial motion. As such, the issue is waived. (People v. Enoch (1988), 122 Ill. 2d 176.) Nonetheless, defendant urges us to review these alleged errors to determine whether they constitute plain error. The plain error rule may be invoked in instances where the evidence is closely balanced, or where the error is of such magnitude that it deprived the defendant of a fair trial. (People v. Fields (1990), 135 Ill. 2d 18, 60; People v. Carlson (1980), 79 Ill. 2d 564, 576-77.) We do not find the evidence against defendant closely balanced, for the State produced overwhelming evidence to prove defendant guilty beyond a reasonable doubt. Nor do we find the complained-of errors so egregious as to have deprived defendant of his right to a fair trial. We therefore reject defendant’s contention that the purportedly improper comments amounted to plain error.
SENTENCING ISSUES
A
Defendant contends that he could not be found eligible for the death penalty under section 9 — 1(b)(7) of the Criminal Code of 1961 (Ill. Rev. Stat. 1985, ch. 38, par. 9 — 1(b)(7)). That section provides that a person convicted of murder may be eligible for the death penalty if "the murdered individual was under 12 years of age and the death resulted from exceptionally brutal or heinous behavior indicative of wanton cruelty.” Ill. Rev. Stat. 1985, ch. 38, par. 9 — 1(b)(7).
According to defendant, his conduct consisted only of omissions and the intimidation of a third party (Hurley) into the failure to act, rather than a physical act. *144Therefore, he claims that his conduct was not exceptionally brutal or heinous and indicative of wanton cruelty. His argument is premised on the assertion that his conviction rested upon an omission, or failure to act, rather than upon his overt acts. As explained in our previous discussion, however, defendant was found guilty of the victim’s murder beyond a reasonable doubt based upon his overt acts. Therefore, we need only consider whether defendant’s conduct that caused the death of the victim can be characterized as "exceptionally brutal or heinous behavior indicative of wanton cruelty,” as required by the statutory aggravating factor. Ill. Rev. Stat. 1985, ch. 38, par. 9 — 1(b)(7).
The phrase accompanied by "exceptionally brutal or heinous behavior, indicative of wanton cruelty” must be given its ordinary and popularly understood meaning. (People v. La Pointe (1981), 88 Ill. 2d 482, 499-500.) As defined, " 'heinous’ ” means " 'hatefully or shockingly evil: grossly bad: enormously and flagrantly criminal’
" 'brutal’ ” means " 'grossly ruthless’, 'devoid of mercy or compassion: cruel and cold-blooded.’ ” (La Pointe, 88 Ill. 2d at 501, quoting Webster’s Third New International Dictionary 1050, 286 (1971).) In general, this court has found brutal or heinous behavior to be present in cases involving prolonged pain, torture, or premeditation. See, e.g., People v. Odie (1988), 128 Ill. 2d 111; People v. Mitchell (1984), 105 Ill. 2d 1.
Defendant’s conduct in deliberately subjecting the 16-month-old victim to starvation and subfreezing conditions over a four-month period comports with the established definition of brutal or heinous behavior indicative of wanton cruelty. Defendant ordered that the victim, along with Victoria and Victor, remain, in a small unheated bedroom in which he opened the window for hours at a time during the winter months of November and December. The victim was dressed only *145in a thin tee-shirt and diaper, and was provided with no blankets or cover. The evidence adduced at trial established that the victim’s exposure to such extreme cold caused her death by profound hypothermia.
Defendant also prevented the victim from receiving adequate nourishment, as he fed her only small portions of infant formula a few times each week. As the victim’s condition deteriorated as a result of the starvation and freezing conditions that she was exposed to on a daily basis, defendant physically prevented the victim’s mother from taking her to the hospital.
We are also mindful of the fact that defendant did not deprive the children of basic life essentials because he had no money. Defendant took Hurley’s paycheck from her when she was paid. Upon defendant’s arrest, he was found with $4,427 in currency in his possession.
Accordingly, we reject defendant’s claim that his death sentence must be vacated. Defendant caused the death of a helpless 16-month-old infant by forced starvation and exposure to subfreezing temperatures over a prolonged period. Without a doubt, such conduct constitutes exceptionally brutal or heinous behavior indicative of wanton cruelty.
B
In a related argument, defendant assigns as error the fact that the jury was not instructed with a narrowing construction of the phrase "exceptionally brutal or heinous behavior indicative of wanton cruelty.” Defendant cites People v. Lucas (1989), 132 Ill. 2d 399, for the proposition that the terms used in section 9 — 1(b)(7) have been construed in other contexts as involving the infliction of prolonged pain or torture, or premeditated behavior on the part of the defendant, and it is on those bases that the aggravating circumstances should be applied. Defendant argues that because the jury did not have the benefit of such a "limiting instruction,” his *146death sentence must be vacated and this cause should be remanded for resentencing.
The State points out that defendant has waived this issue by his failure to object to the tendered instructions and by failure to provide alternative instructions for the court to consider. (Enoch, 122 Ill. 2d 176.) Therefore, this issue is waived.
Even if defendant had properly preserved this issue for review, we are not persuaded by his argument. The record reveals that the jury was adequately instructed that before defendant could be found eligible for a death sentence, the State had to prove that the defendant was over 18 years of age at the time that he committed the murder, that the murdered individual was under 12 years of age, and the death resulted from exceptionally brutal or heinous behavior indicative of wanton cruelty. (Illinois Pattern Jury Instructions, Criminal, No. 7A.11 (2d ed. 1981).) The State presented evidence that established both the victim’s and defendant’s birth dates. The State relied on the facts adduced at trial to prove that defendant caused the victim’s death by intentional starvation and exposure to inclement weather without benefit of adequate clothing or cover over a prolonged period. He also prevented the victim’s mother from obtaining medical care when the victim’s health began to deteriorate. Defendant offered no evidence and made no argument in mitigation at the sentencing hearing.
Under the facts presented here, a reasonable jury certainly could have found all of the elements necessary to satisfy section 9 — 1(b)(7): the victim was under 12 years of age, and defendant’s conduct was not only exceptionally brutal and heinous, but was also indicative of wanton cruelty.
C
Defendant also claims that section 9 — 1(b)(7) is un*147constitutional. However, this court has held that section 9 — 1(b)(7) is not unconstitutional on its face. (Odie, 128 Ill. 2d 111.) Section 9 — 1(b)(7) specifically describes the conduct that qualifies an accused for the death penalty and is not susceptible to arbitrary application. (Odie, 128 Ill. 2d at 140.) Subsequent challenges to this statute in light of the Supreme Court’s decision in Maynard v. Cartwright (1988), 486 U.S. 356, 100 L. Ed. 2d 372, 108 S. Ct. 1853, have also been upheld. See Lucas, 132 Ill. 2d at 444; People v. Kidd (1989), 129 Ill. 2d 432, 455-56; People v. Terrell (1989), 132 Ill. 2d 178; People v. Tye (1990), 141 Ill. 2d 1.
CONSTITUTIONALITY OF THE ILLINOIS DEATH PENALTY
As a final matter, defendant raises a number of challenges to the death penalty statute. We decline defendant’s invitation to revisit the following arguments: (1) the death penalty statute places a burden of proof on the defendant that precludes meaningful consideration of mitigation (People v. Bean (1990), 137 Ill. 2d 65, 138; People v. Whitehead (1987), 116 Ill. 2d 425, 465); and (2) the death penalty statute is unconstitutional because it does not sufficiently minimize the risk of arbitrarily or capriciously imposed death sentences. People v. Spreitzer (1988), 123 Ill. 2d 1, 44.
In his last argument, defendant posits that based upon the Federal district court’s decision in United States ex rel. Free v. Peters (N.D. Ill. 1992), 806 F. Supp. 705, the Illinois death penalty statute is unconstitutional because the jury instructions are confusing and misleading to the jurors. We note, however, that this decision has been reversed by the Seventh Circuit Court of Appeals (Free v. Peters (7th Cir. 1993), 12 F.3d 700). We are persuaded by the sound reasoning employed in that decision. Defendant offers no persuasive reason to disturb that holding.
*148Accordingly, we find no merit to defendant’s challenges to the constitutionality of the Illinois death penalty statute.
CONCLUSION
For the reasons set forth above, we affirm defendant’s conviction and death sentence. We direct the clerk of this court to enter an order setting Wednesday, November 16, 1994, as the date on which the sentence of death, entered by the circuit court of Cook County, shall be carried out. Defendant shall be executed in the manner provided by law. (111. Rev. Stat. 1991, ch. 38, par. 119 — 5.) The clerk of this court shall send a certified copy of this mandate to the Director of Corrections, to the warden of the Stateville Correctional Center, and to the warden of the institution where defendant is now confined.
Affirmed.