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Consider an equivalence relation θ on some set B and a function:

$:^2→ f : B 2 → B $.

We want to lift f to the set of equivalence classes B/θ, i.e., we want to define a function $:(/θ)^2→(/θ) $ canonically in terms of $f$. For this to be meaningful, f has to be θ-consistent. That is, if $f$ is applied to a pair $(_1,_2)∈^2$, the equivalence class $[(_1,_2)]_θ$ may only depend on the equivalence classes $[_1]_θand [_2]_θ $(irrespective of which concrete elements both b_1 and b_2 are within their equivalence classes).

Task: Define the sum of two fractional representations of rational numbers as a function sum: $^2 → A$ (for A = Z × (Z \ {0}) as defined above), using standard addition and multiplication in the integers

I defined a function $+:^2→:[(,)]+[(,)]⇔[(+,)]$

So taking two equivalence classes, this functions provides, unimportant of the rational representation chosen, the sum of two rationals. Could someone help me with this problem as I don't know whether my solution is correct?

Stevo
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    This question and https://math.stackexchange.com/questions/3879232/define-the-sum-of-two-rationals-as-a-function are the exact same. – player3236 Oct 24 '20 at 10:52
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    This is an exact duplicate of this question, posted just a few minutes earlier. (What's up with that?) – Blue Oct 24 '20 at 10:52
  • I didn't know that, but apparently nobody knows the answer... –  Oct 24 '20 at 11:02
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    There might be a different explanation for why no one has posted an answer. – John Hughes Oct 24 '20 at 11:09
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    So, where did you find this question? – Gerry Myerson Oct 24 '20 at 11:16
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    It was also posted twelve hours ago (https://math.stackexchange.com/questions/3878744/question-concerning-equivalence-relations) and then deleted two hours ago. Sounds to me like an question where the asker doesn't want it sitting visible for too long, or thinks that re-asking will get fresh attention, but I'm sure there's a more reasonable explanation. It's funny that all three people who asked the identical question were completely new users. – John Hughes Oct 24 '20 at 11:27
  • @JohnHughes: That third instance was also re-asked by the same author an hour ago. It's quite curious that three instances from three "different" authors end with the same "Could someone help me with this problem as I don't know whether my solution is correct?" (emphasis mine). Something very strange is going on. Flagging for moderator attention. – Blue Oct 24 '20 at 11:29

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