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 20h comment How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$? How do you prove that $y=x$ is that tangent? Apr 3 awarded Nice Question Feb 26 comment How to prove that a polynomial of degree $n$ has at most $n$ roots? It's obvious that $f=(x-a)q$ if $a$ is a root, but how can that be demonstrated? Feb 25 awarded Famous Question Feb 18 awarded Booster Feb 17 awarded Announcer Feb 7 comment How to derive: $\left(1 + \frac{1}{n}\right)^n < 1 + 1 + \frac{1}{2}+…+\frac{1}{2^{k-1}}$ For what $n$ is this supposed to hold? Feb 7 accepted Easy proof, that $\rm e\notin \mathbb Q$ Feb 7 accepted Squaring modulo n — is there a systematic way to generate the fixpoints? Feb 7 accepted How do I show that the probability of the union of events is not larger than the sum of the individual probabilities? Feb 7 comment How do I show that the probability of the union of events is not larger than the sum of the individual probabilities? That's a really good idea. Thank you! Feb 7 comment How do I show that the probability of the union of events is not larger than the sum of the individual probabilities? @NobleMushtak Not quite, we are supposed to show an inequality and the $A_n$ are not necessarily disjoint. Feb 7 asked How do I show that the probability of the union of events is not larger than the sum of the individual probabilities? Jan 1 awarded Yearling Dec 4 comment Can we express the roots of all polynomials in terms of roots of some special polynomials? @theREALyumdub It isn't with just ordinary radicals $\root n\of m$, but with the Bring-radical, you always can (as far as I understood). Dec 4 asked Can we express the roots of all polynomials in terms of roots of some special polynomials? Oct 24 accepted What is the determinant of the sum of a diagonal matrix and a matrix of ones? Oct 19 comment Can we express every partial order with these two combinators? @GitGud Yes, precisely. Oct 19 asked Can we express every partial order with these two combinators? Sep 30 comment How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$? @R R It addresses them in the intuitive sense: Imagine reducing one angle until it becomes zero and then continuing to move the line you moved, that's what the construction for negative angles looks like. For this particular application, it's sufficient to show that $\lim_{x\to0^+}{\sin x\over x}=0$ though (if I recall correctly, it has been some time).