Product over real interval? Is there a better way of putting this?

Asked Apr 06 '15 at 03:17

Active Apr 06 '15 at 03:45

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In my amateur interest, I have arrived at this (nothing rigorous here at all):$$\prod_{a\in [1,2]} \prod_{b=0}^\infty f(a,b) \neq 0$$

For starters, there might be a more intuitive way about doing this. I want to be able to say that $f(a,b) \neq 0, a\in [1,2] \in \mathbb{R}$ for all $b\in \mathbb{R}$

are there any identities that might simplify the two products?
is it even worth specifying the product over a real interval? (For all real numbers between)

NOTE what the function $f$ is, is not what is important here, I'm looking for something more general.

edited Apr 06 '15 at 03:44

mb7744

1,292

asked Apr 06 '15 at 03:17

Sam Walls

Just to be clear is this what you want to express? $\forall a \in [1,2], f(a,b) \neq 0$. If you are unfamiliar with the notation, $\forall$ just means "for all" or "for every."
I don't quite see the point of the 'product.'
– mb7744 Apr 06 '15 at 03:21
The point of the product is just an expansion of what you said ^ that could potentially be helpful – Sam Walls Apr 06 '15 at 03:23
What does the cross denote in terms of sets? – Sam Walls Apr 06 '15 at 03:27
$A \times B = {(a,b) | a \in A, b \in B}$ – mb7744 Apr 06 '15 at 03:28
Yes, that is the innequality given, but what I'm trying to do is expand on that, maybe give something I can test for f – Sam Walls Apr 06 '15 at 03:28
Let us continue this discussion in chat. – mb7744 Apr 06 '15 at 03:29
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This post seems related: A question about $\prod_{x\in \mathbb{R}^{*}}{x}$ – Martin Sleziak Sep 17 '15 at 09:20

Product over real interval? Is there a better way of putting this?

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