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Feb
6
revised Heine definition of limit of a function at infinity using sequences
added 7 characters in body
Feb
6
answered Heine definition of limit of a function at infinity using sequences
Feb
6
answered What is the dimension of $c_0/M$?
Feb
6
revised How many times will the innermost loop be iterated
deleted 4 characters in body
Feb
6
answered How many times will the innermost loop be iterated
Feb
6
comment Is it possible to create a software to find formal proofs?
Yes. But finite does not mean practical or even before the end of the Universe
Feb
6
comment Showing that the inferior integrals of two functions are equal.
Should this be something like essential infimum/supremum?
Feb
6
comment Is there a name for the two parts of a complex number?
Since the individual names are real part and imaginary part it seems like calling them the two parts is adequate, but I don't think that is established. I'd definitely prefer "Write down the real and imaginary part of that number". Better long than ambiguous.
Feb
6
revised Proof that $\{\,\left]a,\infty\right [\mid a\in\mathbb{R}\,\}\cup\{\mathbb{R} \}\cup\{\emptyset \}$ is topology of $\mathbb{R}$
added 15 characters in body; edited title
Feb
6
comment Proof that $\{\,\left]a,\infty\right [\mid a\in\mathbb{R}\,\}\cup\{\mathbb{R} \}\cup\{\emptyset \}$ is topology of $\mathbb{R}$
For the union part, I'd suggest a case distinction: If the union is empty or all of $\Bbb R$ we are done. Only in the remaining case, the inf exist is a real number) and then ...
Feb
6
awarded  Enlightened
Feb
6
awarded  Nice Answer
Feb
6
comment Solve the following congruence: $x(x+1)(x+2) \equiv 0 \pmod{221}$
@DietrichBurde Indeed, that's when we order solutions by "come to mind" instead of "by size" or whatever the OP may possibly intend ...
Feb
6
comment Solve the following congruence: $x(x+1)(x+2) \equiv 0 \pmod{221}$
When you are asked to find the first five solutions, where do you start? Do you want $x\ge 1$ or $x\ge 0$?
Feb
6
answered Solve the following congruence: $x(x+1)(x+2) \equiv 0 \pmod{221}$
Feb
6
revised Last digit of $235!^{69}$
deleted 1 character in body
Feb
6
answered Last digit of $235!^{69}$
Feb
6
comment Proof of derivatives though first principle method
The first principle computation of the derivatives of sine and cosine typically uses addition theorems for these trigonometric functions and somewhere deep inside requires the computation of one single specific limit: $\lim_{x\to 0}\frac{\sin x}{x}=1$. One has to be careful not to fall into circular argumentation at that point! A geometrically inclined proof of that limit typically compares the areas of certain triangles and circular sectors to establish $\sin x<x<\tan x$ for $0<x<\frac\pi2$ or the like.
Feb
6
answered Generate random variate using inverse transform technique of $ f (x) =a (1+|x-2|)$
Feb
6
comment Generate random variate using inverse transform technique of $ f (x) =a (1+|x-2|)$
Your integral over the full domain should simply be a sum, shouldn't it? And what you need should rather be something like $\int_{-1}^xf(t)\,\mathrm dt$, I suppose