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What is infinity?

MathematicsLesson on requestFree to read

Quick answer

Infinity is the idea of something without any end or limit — larger than any number you could ever count to. It's not a number itself but a concept, and mathematicians have shown there are even different 'sizes' of infinity.

Key things to understand

  1. It describes something endless, beyond any finite number.
  2. It's a concept, not a number you can do ordinary arithmetic with.
  3. The counting numbers go on forever — one example of infinity.
  4. Surprisingly, some infinities are 'bigger' than others.
  5. It appears across math, from calculus to set theory.

People also ask

Is infinity a number?
No — it's a concept describing something without end. You can't treat it like an ordinary number in arithmetic.
Can one infinity be bigger than another?
Yes — mathematician Georg Cantor showed the infinity of all decimals is larger than the infinity of counting numbers.
What does infinity look like in math?
It shows up as endless sequences, limits in calculus, and the symbol ∞, representing values that grow without bound.