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

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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 +.
The point to this result is to demonstrate that the positive numbers form a group. The behaviour of real number arithmetic is taken for granted. The point is the closure of the + numbers under multiplication. --prime mover 14:23, 11 May 2011 (CDT)
... but I've added a crucial couple of results that justify it. Good call. --prime mover 14:29, 11 May 2011 (CDT)