Talk:Real Numbers are Uncountably Infinite

It's the same proof, but a bit more pictorial, and slightly more general by omitting the integer part. --Linus44 13:06, 6 March 2011 (CST)


 * Ça plane pour moi --prime mover 15:13, 6 March 2011 (CST)

... but one more thing: what's with the $\hookrightarrow$ notation? --prime mover 15:25, 6 March 2011 (CST)


 * $\hookrightarrow$ for an injection, $\twoheadrightarrow$ for a surjection, when either I feel it needs emphasizing or I feel like having a prettier arrow. --Linus44 16:16, 6 March 2011 (CST)


 * ... completely endorse that - how about a citation, or (better still) add them to the pages for Injection and Surjection? --prime mover 17:12, 6 March 2011 (CST)


 * Any way to render the combination of the two for a bijection, with both the hook and two heads? On an unrelated note, do we really need the min function in $f_n = \min\left\{d_{nn} + 1\right\}$ since it's just the min of one thing (or was that supposed to be a comma instead of a plus?)  --Alec  (talk) 23:36, 6 March 2011 (CST)


 * For a bijection we have $\leftrightarrow$ which gets used occasionally. We have also used $\rightarrowtail$ for injection - clearly these symbols are fairly arbitrary and not de rigueur enough to introduce without defining them each time, e.g. "... where $\twoheadrightarrow$ denotes a surjection" or whatever.


 * I've raised the question of varying notation before (everyone has their own faves and tends to get protective of them) - I wonder whether it's worth specifying the "house style" for various bones of contention. --prime mover 00:31, 7 March 2011 (CST)


 * The $\min$ can go, it was going to allow for $d_{nn}+1 = 10$, but I thought it was simpler to say "cycle modulo 10" and forgot to get rid of the min. There isn't a hooktwoheadarrow that I've seen; you can concoct one:




 * but MathJax doesn't like it. Personally I like $\stackrel{\sim}{\longrightarrow}$ for isomorphisms, that way all three are easy to distinguish in commutative diagrams. --Linus44 03:33, 7 March 2011 (CST)


 * Stumbled across Powerset of Natural Numbers Not Countable and thought another proof was in order. --Linus44 09:16, 7 March 2011 (CST)

I'm not clear on what the function $f$ specified in Another Proof is, but off hand it doesn't look like it would be onto $[0,1]$ if it's based on strings of just 0s and 1s base 10. Can you give a more explicit function? --Alec (talk) 00:54, 8 March 2011 (CST)


 * It's in base 2, not base 10 --Linus44 06:14, 8 March 2011 (CST)