Why Do Infinity And Numbers Behave So Differently?

Imagine you have two bags of candies. One bag has all the numbers like 1, 2, 3, they go on forever. The other bag is even bigger; it has numbers between every single number in the first one, like 0.5, 0.25, and even weird ones like π (pi). Even though both bags are endless, the second one is actually more infinite than the first! Infinity doesn’t behave like numbers we know.

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Examples

You have an endless row of numbers, like counting from 1 to infinity. You also have a bigger bag with all the numbers in between those, that one is even more infinite.
There’s a way to match every number you can think of with even numbers (like 2, 4, 6), but there are more real numbers than just whole ones.
If you write out every number from 0 to 1 and keep adding more, you’ll still miss some, the real numbers never end.

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Categories: Math · infinity· numbers· math concepts· countable infinity· uncountable infinity