How are some infinities bigger than others?

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I was watching Veritasium’s video about math having a fatal flaw. He explained that if we make a set of all the numbers in between 0 and 1, then added one to the first digit of the first number and added one to the second digit of the second number etc, we would always have a new number. He said this proved that there were more numbers in between 0 and 1 than natural numbers.

I was confused as to why you can’t do this with natural numbers, and how that proved one infinity was smaller than another.

In: Mathematics