Talk:Reduced product

Unclear about equivalence relation
I'm struggling to make sense of the significance of Us role in the definition. Is it that the equivalence relation is trivial because removing I from U will leave it empty? Then what's the role of U outside of this set being indexed, and why does that determine its classification? The "such that ai=bi" qualifier is also confusing. Is it saying I is in U? Is it saying ai and i are equivalent if there's an i such that they're equal? If the latter, why isn't it an equivalence between a and b? Filter (mathematics) doesn't explain this notation or its conventions, only using it on occasion, so I'm simply lost. ᛭ LokiClock (talk) 18:49, 9 February 2012 (UTC)