Definition talk:Valuation

Category may not be entirely appropriate; apparently this also crops up in representation theory. However, I have only seen it in number theory (or derivate fields). --Lord_Farin 12:51, 19 March 2012 (EDT)


 * I'm not too sure about $+\infty$. Do we in fact mean $\omega$? --prime mover 15:55, 19 March 2012 (EDT)


 * ... second thoughts we probably don't - but has the concept it represents been rigorously defined? --prime mover 15:56, 19 March 2012 (EDT)
 * $+\infty$ means the positive infinity: $n+(+\infty)=+\infty+n=+\infty$ and $\infty>n$ for all $n\in\Z$.--Dan232 16:04, 19 March 2012 (EDT)

I am planning on defining $+\infty$ rigorously, but in fact it's simply an auxiliary symbol playing the rôle of positive infinity; I think it would be a good idea to put up a page defining $\overline{\Z} = \Z \cup \{\pm\infty\}$ similar to $\overline{\R}$, but I lack a source to do so properly, without my idiosyncrasies. --Lord_Farin 16:17, 19 March 2012 (EDT)