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1d
awarded  Popular Question
Apr
17
revised how to find mininimum $f(x)$ using $\int_{-\infty}^{\infty} f(x)g(x)dx$?
Please don't use \displaystyle in titles for your posts as it breaks the layout of the front page.
Apr
1
revised Difference between one-variable calculus and multi-variable calculus?
deleted 2 characters in body
Oct
28
awarded  Necromancer
Oct
11
answered How discontinuous can the limit function be?
Oct
10
comment How discontinuous can the limit function be?
You might find the Baire-Osgood theorem interesting. (Disclaimer: I wrote up the first version of the page at ProofWiki.) You might also find this question/example interesting.
Sep
20
awarded  Popular Question
Sep
17
comment let $n,k \in \mathbb{N}$. Show that there exist n consecutive natural numbers which are all divisible by a k-th power
LaTeX tips: Use \pmod{k} to get "(mod k)", \mid for the "divides" symbol, and \vdots for vertical ellipsis.
Sep
17
revised let $n,k \in \mathbb{N}$. Show that there exist n consecutive natural numbers which are all divisible by a k-th power
deleted 19 characters in body
Aug
30
awarded  Great Answer
Aug
30
awarded  Nice Answer
Aug
27
comment Example of Topological Vector Space
I think you need to narrow it down a little bit, because the whole space is obviously a convex neighbourhood of each of its points, so any non-locally convex space will satisfy your query.
Aug
17
awarded  Yearling
Aug
6
awarded  Populist
Aug
3
comment What is the meaning of $\exp(\,\cdot\,)$?
Wow. I just noticed that I have written "$\exp(a) + \exp(b)$" instead of $\exp(a) \exp(b)$. What a bizarre typo/matho.
Jul
19
comment Help hint on the following question regarding countable dense set and Lebesgue measure
@amirbd89 what's there to explain? Okay, using a minus sign for set difference might not be the best idea, but other than that it's pretty clear: It's the Lebesgue measure of the complement (in $\mathbb R^n$) of the union of translates of $E$ by elements of $D$.
May
4
comment Prove $\bigcap S$ exists for all $S \ne \emptyset$. Where is the assumption $S \ne \emptyset$ used in the proof?
For example if you instead wrote $\cap S = \{x \in \cup S \mathrel\colon A \in S \implies x \in A\}$, then there would be no problems and you'd have $\cap \emptyset = \emptyset$.
May
4
comment Prove $\bigcap S$ exists for all $S \ne \emptyset$. Where is the assumption $S \ne \emptyset$ used in the proof?
Writing $\{x : \Phi(x)\}$ for some formula $\Phi$ is dangerous (as per Russel's paradox). This is unrestricted set comprehension and is not allowed in ZFC.
May
1
revised What is the number of elements of $\mathbb Z[i] /I $, where $I:=\{a+ib \in \mathbb Z[i] : 2 \mid a-b\}$?
Use \mid for "divides"
May
1
revised What is the number of elements of $\mathbb Z[i] /I $, where $I:=\{a+ib \in \mathbb Z[i] : 2 \mid a-b\}$?
Cleanup and grammar fixes