What does w.l.g mean?

Question

My lecturer has abbreviated something and I can't find what it is. Here is how it has come up in my notes:

Lemma: In any integral domain, $p$ prime $\implies p$ irreducible.

Proof: Suppose $p$ is prime and $p = ab$. w.l.g $p \mid b$. So $cp = b$ for some $c \in R$...

What does that w.l.g bit mean? Does it make sense from there or shall I try and find another example?

It didn't come up in the lecture. I thought I made some mistake in the proof from what she said so I went through her online notes and I saw it there — Kaish, Apr 10 '13 at 12:09

score 12 · Accepted Answer · answered Apr 10 '13 at 12:06

12

W.l.g is a reasonably common abbreviation for "without loss of generality" (used for assuming something without affecting the validity of the proof in general, usually because there are multiple, identical alternatives). Another common one is WLOG.

answered Apr 10 '13 at 12:06

Lord_Farin

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WLOG was in vogue when I was in grad school. – ncmathsadist Apr 10 '13 at 12:50
It used to mean Weiss logarithm :-) – Julián Aguirre Apr 10 '13 at 12:58
5

I have never seen Wlg, but only WLOG. – KCd Apr 10 '13 at 13:07

MJD · Answer 2 · 2013-04-10T12:58:31.230

9

edited Apr 10 '13 at 12:58

answered Apr 10 '13 at 12:10

MJD

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What does w.l.g mean?

2 Answers2