Do numbers continue to infinity?

All About Numbers Read more from
Chapter Math Basics

When most of us think of infinity, we envision the universe continuing on forever; and in mathematics, we often think of numbers that are never-ending. Sometimes it is difficult to understand infinity since our own lives—and most of our experiences—are finite (eventually end). Infinity is a mind-boggling concept.

There are several rules to mathematical infinity—the three most important are: no matter how high you count numbers, you can always count higher; no matter what length you draw parallel lines, they will never meet; and when starting with a line, dividing it in half, then dividing that in half, and so on, you will never stop dividing the resulting line segment.

Even though scientists and mathematicians agree that infinity exists theoretically, it is often a difficult concept to understand and accept. Is it true that the number of particles in the universe are infinite? Does the universe continue on forever? Do parallel lines eventually meet at a place we have yet to discover? If a particle is infinitely divided, just how small can an atomic particle become? And to add to the unimaginable explanations, German mathematician George (Georg) Ferdinand Ludwig Philipp Cantor (1845–1918) mathematically reasoned out that not only do infinities come in different sizes, but there are an infinite number of infinities.


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