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If you understand what it is used for, you'll understand why it is important. "Infinity" is used with somewhat different meanings in different context. For example:

  • In calculus, it means that the value of a variable or function grows without bounds, i.e., there is no limit to how high it can be. In this case, "infinity" is not properly a number; it is more like a tendency.
  • In set theory, "infinity" refers to the size of sets - for example, the set of integers, or the set of real numbers. It turns out that in this case, there are different infinity, i.e., some are larger than others.
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Q: Why is infinity important?
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