> The cantor space is uncountable (which can be seen by prepending '0.' before every binary sequence which gives the real number interval [0,1).)
You can do the same trick with natural numbers to "prove" that they are uncountable too - just drop the duplicates. 0.0, 0.1, 0.2, 0.3, ... 0.9, 0.11, 0.12, 0.13...
Unfortunately, neither of these sequences contain the real 1/3, so they have gaps.
You can do the same trick with natural numbers to "prove" that they are uncountable too - just drop the duplicates. 0.0, 0.1, 0.2, 0.3, ... 0.9, 0.11, 0.12, 0.13...
Unfortunately, neither of these sequences contain the real 1/3, so they have gaps.