Why are the Reals uncountable?

No.12571000 ViewReplyOriginalReport
Why are the reals uncountable? It is proven that every real number has a decimal expansion, right? So couldn’t we just slowly count each and every possible decimal expansion? We start with one digit combinations, assigning each digit to some integer, and then moving to two digits, and so on. Wouldn’t this be a one-to-one correspondence with the positive integers?