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 Apr 11 reviewed Approve Right and left hand limits. Apr 8 comment What does this notation mean? $x \mapsto f(x)$ @YoTengoUnLCD: if you consider it tautologous, fair enough. (But there are people who would write their functions as $x\mapsto xf$ or $x\mapsto x^f$ or similar. Not stating this can lead to genuine confusion - does $fg$ mean "do $f$ then $g$" or "do $g$ then $f$"? Writing explicitly that you will denote the image of $x$ under $f$ by $f(x)$ avoids this potential confusion. Also, for instance, with more arguments, you might write $g(x,y)$, but would prefer to write $x*y$ rather than $*(x,y)$; writing this out explicitly avoids confusing your reader.) Apr 8 comment Find all Gaussian integers $α, β, γ$ such that $αβγ = α + β + γ = 1$ "If any of α,β,γ are equal from that list they cannot add to 1" - apart from the case (1,1,-1) which is easily checked to fail. Mar 27 reviewed Approve Let f(x),g(x) be complex polynomials, if f(x) | g(x) and g(x) | f(x) then.. Mar 27 comment Does a terminating recurrence relation diverge? As you've noticed, the expression $u_{k+1} = \frac{4}{u_k + 2}$ doesn't make sense when $k = 6$ (so there should really be a caveat in the definition). What is your definition of 'sequence', and does $\{u_k\}$ fit it? If this isn't even a sequence (in this case, because it fails to be infinite), it doesn't make sense to ask whether or not it converges. Mar 27 comment Can I make an assumption about arbitrary numbers in a proof? No, you may not assume anything that you can't prove (or your lecturer / teacher hasn't proved). Can you prove that $Q$ exists? (Hint: try to find $P_1$ with $P_1(x_1) = y_1$ and $P_2$ with $P_2(x_2) = y_2$, and combine them somehow to find $P$ with $P(x_1) = y_1$ and $P(x_2) = y_2$.) Mar 27 reviewed Reject What is the intuition behind / How can we interpret the eigenvalues and eigenvectors of Euclidean Distance Matrices? Mar 27 reviewed Approve Expressing an integral in closed form Mar 27 comment Let f(x),g(x) be complex polynomials, if f(x) | g(x) and g(x) | f(x) then.. @MattSamuel Depends on your definition of "divides", surely? In a commutative ring (here $\mathbb{C}[x]$) the natural definition seems to me to be "$g|h$ iff there exists $f\neq 0$ with $fg = h$". If you want to make an exception for $0$ somewhere, go ahead, but definitions vary from author to author, so a discussion of which is correct doesn't seem all that useful. I just flagged it up as a potential issue. Mar 27 answered Let f(x),g(x) be complex polynomials, if f(x) | g(x) and g(x) | f(x) then.. Mar 27 reviewed Reject help me understand this given solution from gelfand algebra text. Jan 16 comment Why are primes considered to be the “building blocks” of the integers? @zod Edited, thanks! Jan 16 revised Why are primes considered to be the “building blocks” of the integers? edited body Jan 13 awarded Nice Answer Jan 11 comment $X^2$irreducible but not prime (Are $X$ and $x$ the same thing, and do you mean $X^i$ instead of $X_i$?) $X^2$ certainly looks prime here to me. Jan 11 answered Reverse Product Rule ODE Jan 11 reviewed Approve $2\times 2$ matrices forming the Klein $4$-group. Jan 11 revised Why are primes considered to be the “building blocks” of the integers? added 44 characters in body Jan 11 answered Why are primes considered to be the “building blocks” of the integers? Jan 11 comment Group Duality with respect to Generators and Relations (2/2) On the other hand, there certainly are some notions of duality that arose from mathematical questions, which you may be interested in looking up. A simple one would be the concept of a dual vector space (vector spaces are, of course, continuous groups too), which arises by considering functions on that space (or matrix transposition). A harder one: Pontryagin duality comes from trying to do Fourier analysis on certain groups, and crops up very naturally in a bunch of places, including e.g. the character theory of finite abelian groups.