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
> He explained that if we make a set of all the numbers in between 0 and 1
Not just a set, a list. It has to be well-ordered for the proof to work. There has to be a first number and a second number and so on. They can’t all be in a disorganized heap.
Remember, the point of the proof is to show that such a list is *impossible.* The argument is, no matter what list you present, his method will find a Real number 0 < x < 1 that isn’t on the list.
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