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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
11
comment How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?
While this is indeed an interesting approach, integrals haven't been taught at the point where this limit is proved. Thank you for your answer though.
Mar
23
comment What is the lower bound for an algorithm that reconstructs a permutation?
I fixed a couple of typos. I'm sorry if that changes your answer.
Mar
13
comment How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?
Indeed, it's easy to see that this holds if one uses a series, but this question starts on the prerequisite that one does not use a series.
Mar
3
comment Is there a totally ordered set we can map any other totally ordered set to?
I edited the question because I thought that the case $|O|=|\mathbb N|$ might be interesting, too. Thank you for researching this!
Mar
3
comment Is there a totally ordered set we can map any other totally ordered set to?
@AndresCaicedo Thank you. I'll see if my university's library has that.
Dec
8
comment How to construct a polynomial from a radix-term?
Ah yes, that makes sense. I'm sorry for my confusion.
Dec
8
comment How to construct a polynomial from a radix-term?
That was a typo, it should have been $\alpha\in\mathbb Q\setminus\{0\}$. I'm a bit confused about how you explain the translation that makes a polynomial $p'$ with $p'(\alpha^{-1})=0$ from a polynomial $p$ with $p(\alpha)=0$. Your explanation does not really enlightens me. Maybe that's just because I am a bit hungover.
Dec
8
comment How to construct a polynomial from a radix-term?
I'm afraid I might have misunderstood something, but what guarantees that $\alpha\in\mathbb Q\{0\}$? Isn't $\alpha$ the value of an arbitrary algebraic expression with $\alpha\neq0$?
Dec
8
comment How to construct a polynomial from a radix-term?
What do you do if we take a negative power over a subterm?
Dec
8
comment How to construct a polynomial from a radix-term?
How can we prove that for every polynomial with integer coefficients $\sqrt 2$ is a root of, $-\sqrt 2$ is a root, too?
Dec
8
comment How to construct a polynomial from a radix-term?
@HenningMakholm Ah, that makes sense. Thank you for pointing out the correct term.
Nov
27
comment Showing that $\lim_{x\to\infty}\left(\sqrt{x^2+c}-x\right)=0$
I feel dumb now.
Nov
11
comment How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?
In a triangle $ABC$ with right angle in $ACB$ we define $\sin BAC=BC/AC$. This is the “geometrical” definition for $\sin$ we used.
Sep
24
comment Reducing the time to calculate Collatz sequences
@sp1rs No. See the answers linking here.
Jun
10
comment How and why did Weierstrass $\wp$ get its special symbol?
It's basically a cursive / script p.
Jun
8
comment How can I make this recurrent equation non-recurrent?
@hardmath Yes, that's what I'm trying to do. I just saw myself how trivial this question is.
Oct
20
comment How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?
It's nice that you post an answer that was literally posted as the top comment to this question.
Oct
16
comment How can I find a point where an osculating circle goes through a certain point?
@Lays I couldn't find an answer to my question on the page you linked. Please note, that $P$ usually does not lay on $f$.