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,
If you take a natural number, and change one of its digits after the decimal place, you don’t get another natural number. If you start with, say, 3, and change the ten thousandths place, you get 3.0001, which isn’t a natural number— so it’s not a problem that it’s not found on your list of all the natural numbers.
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