Why Are There Infinite Numbers?

Imagine you have a never-ending bag of marbles, that’s like infinite numbers. Now, say there are two bags: one with marbles and one with jellybeans. If they’re both never-ending, it might seem like they have the same amount. But what if one bag has more marbles than jellybeans even when both are infinite? That means some infinities are bigger than others, and that’s pretty wild!

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Examples

  1. You can match every jellybean in an infinite bag with a marble from another infinite bag, but you might still have more jellybeans than marbles if the bags are different sizes.
  2. Imagine counting your toys forever, and then starting again, even though both sets of numbers go on forever, they’re not the same size.
  3. There’s an infinity of whole numbers (1, 2, 3…), but there’s also a bigger infinity of decimals (0.1, 0.23, 0.45678…).

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Categories: Math · infinity· numbers· math concepts