The short answer is yes, and I, like the author, don't really understand why so many people spend so much time trying to show that Cantor's proofs are wrong.<p>Cantor's second proof generalises to show that given any set, X, the collection of functions<p><pre><code>  { f: X -&#62; {0,1} }
</code></pre>
is of size strictly larger than X.<p><pre><code>  |{f: X -&#62; {0,1}}| &#62; |X|
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The proof that the reals are uncountable is just this, with the set X as the set of natural numbers.