User talk:TricksterWolf

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 * --Your friendly ProofWiki WelcomeBot 14:15, 20 November 2011 (CST)

Finite Induction
I see where you're coming from on those latest edits on the Principle of Finite Induction (now I look at what I originally had, it does seem wrong to me).

But I wonder whether it's round the wrong way: should it be $S \supseteq \N \setminus N_k$ and $S \supseteq \N^*$? See what I mean? --prime mover 16:01, 20 November 2011 (CST)


 * I see what you mean, but note that for each of the definitions it begins with the supposition that $S \subseteq \N$. This means that $S$ cannot contain anything that is not contained in $\N$, by definition.  The changes I made allow for $S$ to (possibly) contain other members of $\N$ that are not forced by the induction which starts at $k$, rather than automatically excluding them.  :)  Let me know if that's clear. TricksterWolf 23:53, 20 November 2011 (CST)


 * No it's not.


 * Suppose $S = \{5, 6, 7, \ldots\}$ and $k = 6$. Then $S \subseteq \N$ but $N \setminus N_k$ = $\{6, 7, 8 \ldots\}$.


 * Cleary $S \supseteq \N \setminus \N_k$. --prime mover 00:26, 21 November 2011 (CST)


 * Ah, you're right. I'd briefly considered doing it that way and became confused because it seemed to contradict the assumption.  I'll make the change. TricksterWolf 01:07, 21 November 2011 (CST)