Infinity

Infinity is the idea of something that never ends. It is not a regular number you can count to. Instead, it is what mathematicians use when a list, a distance, or an amount keeps going forever. The symbol for infinity looks like a sideways number eight: ∞. A British mathematician named John Wallis first used this symbol in 1655.

You can get a feel for infinity by counting. Start at 1. Then 2, then 3. No matter how high you go, you can always add one more. There is no biggest number. If someone says a billion, you can say a billion and one. If they say a trillion, you can say a trillion and one. The whole numbers go on without stopping. That endless line of numbers is one example of infinity.

Infinity shows up in many parts of math. The number pi, which describes circles, has decimal places that never end and never repeat. A straight line in geometry has no ends. It stretches forever in both directions. Even between two regular numbers, like 0 and 1, there are infinitely many fractions. You can keep cutting the space in half, then in half again, forever.

Here is something strange. Not all infinities are the same size. In the late 1800s, a mathematician named Georg Cantor proved that some infinities are bigger than others. The infinity of whole numbers (1, 2, 3, and so on) is smaller than the infinity of all decimal numbers between 0 and 1. Many other mathematicians at the time thought Cantor was wrong, or even crazy. Today his ideas are a normal part of math.

Infinity also shows up outside math. Scientists ask whether the universe is infinite. We can only see the part of space whose light has had time to reach us, about 46 billion light-years away. Beyond that, we genuinely do not know. The universe might end somewhere, or it might keep going forever. Inside a black hole, equations predict a point where space curves infinitely, but most physicists think this just means our equations break down there.

Infinity can feel strange because nothing in everyday life is truly endless. A bag of candy runs out. A song ends. Even mountains slowly wear away. Infinity is a tool the human mind invented to describe what would happen if things did not stop. It is one of the most powerful ideas in all of math.