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Aug
22
awarded  Yearling
Aug
21
comment What is the most significant digit?
I think you mean leading zeros. Trailing zeros can be significant, but there aren't any here.
Aug
15
comment Consending logic gates
Rather than try to apply equivalence laws to the expression, I'd probably either use a truth table or formally prove each expression from the other.
Aug
15
comment Consending logic gates
"(X AND (X OR Y)) <=> (X AND Y)" - what? No. (X AND (X OR Y)) <=> X.
Aug
15
comment Do the medians (or other cevians) form all the triangles?
But can any 3 lengths satisfying the triangle inequality be a triangle's medians? I'm pretty sure that's what the question is asking. It's confusingly worded, though.
Aug
11
comment Why does the square root of an inverse function turn negative?
Why do you think $-\sqrt x$ is the inverse of $x^2$? This function doesn't actually have an inverse.
Aug
11
comment Square-wise distance
@TheGreatSeo: It's taxicab geometry at a 45 degree angle.
Aug
9
awarded  Fanatic
Aug
8
comment What is the oldest open problem in geometry?
Typo: "no-body problem". At least classically speaking, that one is thoroughly solved.
Jul
29
comment We have $100$ balls (numbered $1,2,\cdots,100$) and $50$ boxes (numbered $1,2,\cdots,50$).
$\Pr(X_i)=1$ should say $\Pr(X_i=1)$.
Jul
29
revised Proving that a poset can be expressed as a union of subchains.
added 230 characters in body
Jul
29
comment Proving that a poset can be expressed as a union of subchains.
@user162369: That said, you seem to be on the right track. A more rigorous statement of why you can join the chains along the antichain is necessary, though.
Jul
29
comment Proving that a poset can be expressed as a union of subchains.
@user162369: StackExchange isn't designed for this kind of interaction; it's based on an ask-question-get-answer interaction model, not extended conversations. Edits like the kind you're making invalidate existing answers. If you want someone to check your work and keep checking it as you modify it, you could try the chat.
Jul
29
comment Proving that a poset can be expressed as a union of subchains.
@user162369: No, because then those two elements of the antichain would be comparable.
Jul
29
comment What is subtraction?
The distinction you're making doesn't seem significant. You're looking at something two equally-valid ways and asking which one is right.
Jul
29
comment Proving that a poset can be expressed as a union of subchains.
@user162369: Try building two smaller sets, one with all elements higher than the antichain removed and one with all elements lower removed, and try to apply the inductive hypothesis to those sets. The case where one of these subsets is the whole set has to be handled separately.
Jul
29
comment Proving that a poset can be expressed as a union of subchains.
@user162369: Sorry, misremembered the proof. I've looked it up now, so the new hint should work better. I'm afraid your modified proof doesn't work, and bof's poset is a counterexample.
Jul
29
comment Proving that a poset can be expressed as a union of subchains.
@user162369: The proof I know works by induction. Try splitting the set along the antichain into "upper" and "lower" pieces.
Jul
29
comment Proving that a poset can be expressed as a union of subchains.
@bof: I tried to come up with an example like that, but I didn't think of anything. I've replaced the example with yours, as yours is much better.
Jul
29
revised Proving that a poset can be expressed as a union of subchains.
Better example suggested by bof