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 Yearling
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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).
Aug
24
comment How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?
@Asker123 No, because ${\sin 0 \over 0} = {0\over 0}$ and you cannot divide by $0.$ A graphing calculator has finite precision, what tells us that the $0$ it displays isn't actually a $0.000000000000000000012445823?$
Jul
3
comment How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?
@goblin The goal is to go from an intuitive understanding of $\sin$ as a geometrical relationship to a function. Using such an implicit definition would be quite dissatisfactory to a student.
May
8
awarded  Popular Question
Apr
17
comment What is the determinant of the sum of a diagonal matrix and a matrix of ones?
@HagenvonEitzen When exactly one entry in the diagonal is $1$, the result is $\prod_i(a_{ii}-[a_{ii}\neq1]),$ where $[p]$ is the Iverson bracket. If more than one entry is $1$, the result is $0$.
Apr
17
comment What is the determinant of the sum of a diagonal matrix and a matrix of ones?
@deinst I think that covers it. Would you mind copying the relevant part of that answer into an answer to this question so I can mark this as accepted? I can do this myself, too, if you don't want to.
Apr
17
revised What is the determinant of the sum of a diagonal matrix and a matrix of ones?
Get rid of a pesky typo