- #1
cragar
- 2,552
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I was reading the book one, two , three ... infinity . And he says that their are the same amount of points on a line as their are in a square. A line from 0 to 1 and then a 1x1 square.
He says when can represent any point in that square with 2 numbers like coordinates. And if we add these numbers together then we can draw a one to one correspondence between the numbers in the square and the line. But then couldn't I just add all the reals from 0 to 1 and then 1 to 2 , and then put these into a one to one correspondence with the natural numbers.
Or does this not work because they are uncountably infinite.
He says when can represent any point in that square with 2 numbers like coordinates. And if we add these numbers together then we can draw a one to one correspondence between the numbers in the square and the line. But then couldn't I just add all the reals from 0 to 1 and then 1 to 2 , and then put these into a one to one correspondence with the natural numbers.
Or does this not work because they are uncountably infinite.