- #1
robertjford80
- 388
- 0
I'm aware of Cantor's diagonal argument but can't you prove the uncountability of reals between 0 and 1 using a simpler method? For instance, take the number .1 sooner or later in order to get a list of the reals between 0 and 1, you're going to have to get to .2 but before you can get to .2 you have to write .11 on your list then before you can get to .12 you have to write .111. In other words if you're obligated to open up a new decimal place then you'll never get to .2