# Talk:Strictly Positive Real Numbers under Multiplication form Uncountable Abelian Group

Just asserting that $ab > 0$ feels non-rigorous. Isn't that essentially what we're trying to prove here? --Alec (talk) 02:15, 11 May 2011 (CDT)
I think Real Numbers form Totally Ordered Field and $(2)$ of Definition:Ordering Compatible with Ring Structure would cover it --Linus44 03:33, 11 May 2011 (CDT)
We already know that $\R$ is a field, and therefore a ring, and so from one of the results in there we know that + times + equals +.