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May
8
comment Properties of power series and their analytic continuation
Other properties such as "is nonzero" are problematic of course.
May
8
answered Let $f(x)=\frac{f(x+e)+f(x-e)}2$. Show that $f$ is affine
May
8
answered How to find if the sum of periodic function is periodic?
May
8
answered Is $\mathbb R[x] / \langle x^2+1 \rangle = \mathbb R[x] / \langle x^2+2 \rangle$?
May
8
comment Can someone explain this notation of a limit?
The notation is of course abusive and thereby confusing. We should be allowed to replace any subexpression by an equal expression in any equation. Thus $a+0=a-0=a$ would "officially" make $\lim_{x\to a+0}=\lim_{x\to a-0}=\lim_{x\to a}$. What shold we think of $\lim_{x\to 0+a}$ or $\lim_{x\to \frac a2+0+\frac a2}$?
May
8
comment Is $\mathbb R[x] / \langle x^2+1 \rangle = \mathbb R[x] / \langle x^2+2 \rangle$?
Are all instance of $R[x]$ meant to be $\mathbb R[x]$?
May
8
comment $\sup A = \inf B$ implies $\forall\varepsilon>0.\exists a\in A, b\in B. b-a<\varepsilon$
There is one special case that needs to be observed. Often one writes $\sup\emptyset =-\infty$ and $\inf B=-\infty$ if $b$ is not bounded from below. Or $\sup A=+\infty$ if $A$ is not bounded from above and $\sup\emptyset=+\infty$. If one allows these cases, they provide counterexamples. (Officially, $\inf$ and $\sup$ do not exist for these sets)
May
8
answered Proving something is primitive recursive
May
8
revised Determine the smallest number P
rolled back to a previous revision
May
8
comment Prove a relation is a equivalence
See now why it is necessary to specify whcih set we are talking about? If $a=\frac12$ were in the set, then $a+a=1$ odd, hence $a\not\sim a$.
May
8
comment Prove a relation is a equivalence
An equivalence relation on which set?
May
8
answered Limit of a sequence involving roots
May
8
answered How to solve the equation $n^2 \equiv 0 \pmod{584}$?
May
8
answered Finding polynomial from sum and product of zeroes
May
8
comment Graph Theory proof: Let G be a planar graph that doesn't contain K3…
Again, without modifier one should silently assume that graph means undirected graph.
May
8
answered Show a continuous bijection cannot have periodic points of prime period greater than 2
May
8
answered How many different right triangles are possible with the shorter side of odd length?
May
8
answered Check if the number is a result of multiplying two fibonacci numbers
May
8
answered Distinct roots of a function
May
8
answered Relate $n$ with $2$