Comments on In "if and only if" proofs, why's 1 direction easier to prove than the other?
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In "if and only if" proofs, why's 1 direction easier to prove than the other?
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This list on Math StackExchange instantiates (biconditional) logical equivalences where one direction can be proved swimmingly, but the other direction is racking to prove. If two propositions are equivalent, why can't they be proved with the same level of difficulty?
Please don't troll with frivolous "proofs" like
This Reddit thread instances two common cases like Hall's Theorem, and a sequence of complex numbers converges $\iff$ it is Cauchy ($\Leftarrow$ is effortless, but $\Rightarrow$ is grueling).
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