Content deleted Content added
Endomorphic (talk | contribs) |
Endomorphic (talk | contribs) |
||
Line 619:
You may very well wonder what it means for an indefinitely proceeding sequence like s_0 to be "one single" sequence throughout. This is fair. I think it does not matter: in whatever sense the list is "one single" list, s_0 will be "one single" sequence in the same sense. And at a minimum, you must admit such a list can be given by a some sort of fixed rule, and then s_0 will be also given by the same sort of fixed rule, and it will never appear in the list, no matter how far it is extended. So at a minimum we conclude that no sort of fixed rule of lists all, and only, the sequences of 0's and 1's given by that same sort of fixed rule. While it may not cause you to enter Cantorian Heaven, this aspect of the argument is in fact quite correct. --[[User:Unzerlegbarkeit|Unzerlegbarkeit]] ([[User talk:Unzerlegbarkeit|talk]]) 00:21, 2 June 2008 (UTC)
:Where did I say that "the set of all infinite sequences of 0's and 1's is not a so-called 'completed infinity'"? --[[User:Trovatore|Trovatore]] ([[User talk:Trovatore|talk]]) 03:41, 2 June 2008 (UTC)
::The article 66.67 seems to be drawing from can be found here: [http://homepage.mac.com/ardeshir/ArgumentAgainstCantor.html] (pulled from [[Talk:Controversy_over_Cantor%27s_theory]]). It's a nasty peice of work, I'm not recommending anyone try to read it (it's really that nasty), I'm just including it for completeness, since wikipedia is about references.
::I'm not sure you'll be able to find any mathematician who denies that "completed infinities exist", nor that Cantor's work is valid. Want to be able to take limits? That needs infinity. Set theory? topology? measure theory? functional analysis? even basic calcules? Lots of "completed infinities" all over the place. You know what: a single decimal expansion *itself* needs "completed infinity", since it's
<pre>
\lim_{n \rightarow \infty} \left( \{sum}_{i=1}^{\n} \frac{a_i}{10^i} \right)
</pre>
::where 'a_i' is an infinite sequence within N \cap [0,9]. [[User:Endomorphic|Endomorphic]] ([[User talk:Endomorphic|talk]]) 18:40, 21 August 2008 (UTC)
| |||