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
>I was confused as to why you can’t do this with natural numbers, and how that proved one infinity was smaller than another.
Every natural number has a finite number of digits. Every irrational number has an infinite number of digits. If you tried this with natural numbers you’d quickly run out of digits to change.
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