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Aug
22
comment Does Darboux property imply strong Darboux property?
That's a classical trick: You start with an object with fancy properties and try to deform it to the extent of losing some of them and preserving others. The rest was trial&error, as the edit history shows.
Aug
21
comment Does Darboux property imply strong Darboux property?
Incidentally, the assumption that $V$ is infinite is unnecessary and can be weakened to $V$ being nonempty, while it seems to me that the condition ${\sf d}^\ast(V) = 0$ can't be relaxed so easily.
Aug
21
comment Does Darboux property imply strong Darboux property?
Fair enough, there was a serious mistake. I gave it another try: hope I will be luckier. (Btw, you may want to read simple.wikipedia.org/wiki/Exempli_gratia.)
Aug
21
revised Does Darboux property imply strong Darboux property?
Fixed (?)
Aug
21
comment Does Darboux property imply strong Darboux property?
You should tell me who is your $V$: You may find it unbelievable, but I can't read your mind!
Aug
21
revised Does Darboux property imply strong Darboux property?
deleted 90 characters in body
Aug
21
revised Does Darboux property imply strong Darboux property?
deleted 90 characters in body
Aug
21
revised Does Darboux property imply strong Darboux property?
deleted 90 characters in body
Aug
21
revised Does Darboux property imply strong Darboux property?
added 63 characters in body
Aug
21
revised Does Darboux property imply strong Darboux property?
Changed "ultrafilter" to "free ultrafilter" and added a reference
Aug
21
answered Does Darboux property imply strong Darboux property?
Aug
6
revised Non-additive upper logarithmic density: $\ell^\star(X \cup Y) \neq \ell^\star(X)+\ell^\star(Y)$
simplified the exposition and fixed a typo
Aug
6
revised Non-additive upper logarithmic density: $\ell^\star(X \cup Y) \neq \ell^\star(X)+\ell^\star(Y)$
added 9 characters in body
Aug
6
answered Non-additive upper logarithmic density: $\ell^\star(X \cup Y) \neq \ell^\star(X)+\ell^\star(Y)$
Apr
8
answered Non-empty intersection between a compact and an unbounded connected subset of $\mathbb{R}^d$
Dec
31
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Dec
31
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Dec
6
awarded  Yearling
Dec
6
awarded  Yearling
Aug
10
comment Prove : $\frac{\cos(x_1) +\cos(x_2) +\cdots+\cos(x_{10})}{\sin(x_1) +\sin(x_2) +\cdots+\sin(x_{10})} \ge 3$
Af for your P.S., try with the tag \tag{put_here_a_label} at the end of your equations.