Fans of Buzz Lightyear know that his catchphrase is “To infinity…and beyond!” But is it even possible to go to infinity? Or beyond it? And exactly what is infinity, anyway?
If you think about a basic number line from your math class, you know that there’s no end to it. In both directions — positive and negative — it goes on forever. That “forever” is called infinity.
The concept of infinity is used mainly in the fields of mathematics and physics to refer to a quantity without end. In fact, infinity comes from the Latin word infinitas, which means “unboundedness.”
Mathematicians and physicists use a special symbol for infinity:∞. This symbol is sometimes called the lemniscate, which comes from the Latin word for “ribbon” (lemniscus).
John Wallis began using this symbol for infinity in 1655. Some believe he based it upon the Roman numeral for 1,000, which was often used simply to mean “many.” Others believe the symbol was based upon the last letter of the Greek alphabet: omega.
In mathematics, infinity has many applications. For example, the mathematical constant known as pi is an infinite decimal. But infinity is more than just a really large number.
Would you believe that there can be different sizes of infinity? It’s true! Consider this: there are an infinite number of positive whole numbers. There are also an infinite number of even positive whole numbers. Even though the number of positive whole numbers and even positive whole numbers are both infinite, the set of infinite positive whole numbers is twice as large as the set of infinite even positive whole numbers!
The concept of infinity is also popular with cosmologists who study the size of the universe. Does space simply go on and on forever without end? That is a question that remains unanswered. What scientists do know, though, leads many of them to believe that the universe may be infinite.
Beyond physics and mathematics, the concept of infinity can also have philosophical applications. For example, the infinite monkey theorem states that a monkey randomly hitting keys on a typewriter for an infinite amount of time will eventually type a given text, such as Moby Dick or the complete works of Shakespeare.
Some people use the infinite monkey theorem to suggest that, if given an infinite amount of time, anything is possible. Experts in statistics and probability, however, have shown that the theorem is actually better proof for how unlikely such events are. For example, the actual likelihood of a monkey exactly typing a complete work, such as Shakespeare’s Hamlet, is so tiny that, even given a period of time as long as the age of the universe, the probability is nearly zero!