Hagen von Eitzen
Reputation
398/400 score
 5h comment Is $\Bbb Q[x]/(x^2+x)$ isomorphic to $\Bbb Q[x]/(x^2-x)$? @mathshungry Because $x\mapsto -x$ takes $x^2+x$ to $x^2-x$. And yes for your interpretation. 7h comment What should I have learnt as an undergraduate? I'd say, You should know where to find information you may lack ... 8h comment Prove that the sum of the squares of two odd integers cannot be the square of an integer. This is quite fine. For completeness you might want to add that an even square must be the square of an even number / divisible by 4.-- Anyone more experienced might have remembered that odd squares are $\equiv 1\pmod 8$, hence the sum of two such is $\equiv 2\pmod 8$, which cannot be square. Your argument boils down to working $\pmod 4$, which is in fact sufficent 10h answered Is $\Bbb Q[x]/(x^2+x)$ isomorphic to $\Bbb Q[x]/(x^2-x)$? 11h revised Why formulate continuity in terms of pre-images instead of image? added 18 characters in body 12h awarded Nice Answer 12h comment is this $f(x)$ continuous at almost every point of an interval $[a, b]$. Of course, why not? 13h comment What is the difference between ≎ and ≏? 13h answered What is the logic underlying this proof? 13h comment $a,b,c,d\ne 0$ are roots (of $x$) to the equation $x^4 + ax^3 + bx^2 + cx + d = 0$ @πr8 If I'm not mistaken, we arrive at $2b^3a^4 + (b^4 + 2*b)a^3 + 3b^2a^2 + (b^3 - b + 1)a + b=0$ as condition for $a,b$. Playing around it seems that e.g. $b=1$ allows rational solutions for $a$ namely $a=1|-1|\frac12$, then $c=-1|1|2$. Only the last case leads to non-zero $d$. I have not guessed other solutions yet 14h comment Is $\{ a_{m}(n) | a_{m}(n)$ with all even digits$\}$ finite set for all $m$? So a simpler(?) preliminary question might be: Is there any $m$ for which it is known whether $X_m$ is finite or infinite? 16h comment Die that never rolls the same number consecutively Interestingly, the third roll is a bit more likely to equal the first roll ... 17h answered Prove that $a . g = g^{-1}.a$ and $g . a = a . g^{-1}$ hold for any group and any action defined. 17h comment Is $\{ a_{m}(n) | a_{m}(n)$ with all even digits$\}$ finite set for all $m$? Do you even know any $m$ for sure where $X_m$ is finite? 17h answered How to differentiate something with u and x? 18h comment Proof for Urysohn's lemma. But the intuition part of that lemma is not that hard, I suppose: The idea is to construct a continuous functoin $\to[0,1]$ as a limit of finer and finer staircase functions. The ability needed to refine a staircase function is precisely the condition in the premise of the lemma. 19h comment Find a **bijection** between two intervals Once the intervals are corrected, try maps of the form $x\mapsto ax+b$ 21h comment How to Calculate Flat rate using Effective Rate? If this is about nominal interest vs. effective interest, this is confusing - a factor near 2 is nearly impossible for bearable rates 1d comment Can we find prime numbers with any sum of digits (except those divisible by three) The approximately $10^n/n \ln 10$ primes below $10^n$ all have $sd_{10}\le 9n$, so there should be plenty of opportunities to "hit" any allowed value ... 1d comment Straight Edge - Only Geometric Construction @Henry I'll have to think about that with a real sketch before me - I just took the validity of the construction in the referenced answer for plausibly granted ...