Reputation
11,088
Top tag
Next privilege 15,000 Rep.
Protect questions
Badges
2 22 48
Impact
~219k people reached

May
17
comment What is a mathematical object?
Why do you restrict "the language of mathematics" to first-order logic? In which language is the Lowenheim-Skolem theorem formulated and proven?
May
16
comment Properties of Intersection of Sets
@GregoryGrant: I know what $2^A$ means, basically because I learned it here on math.SE. Before that, I didn't (but I definitely knew what a power set is, and knew the notation $P(A)$ for it).
May
16
comment Properties of Intersection of Sets
@GregoryGrant: Then you would think wrong.
May
16
comment Properties of Intersection of Sets
@GregoryGrant: Not necessarily more people, just another set of people.
May
15
comment What function satisfies $f(x)+f(−x)=f(x^2)$?
Actually the question doesn't specify the domain. So also the function $f:\{-1,1\}\to\{0,1\}$ with $f(-1)=0$ and $f(1)=1$ satisfies the given requirements.
May
15
comment Notation problem in integration: write $dx$ or ${\mathrm{d}}x$?
@ChristianBlatter: What's wrong with $\sin n\pi$? I'm no mathematician, and I don't see anything wrong with it.
May
14
comment What should be the intuition when working with compactness?
This is a link-only answer. Link-only answers are frowned upon because the link can (and indeed, over sufficient time is almost guaranteed to) become invalid. For example, the file you link to is obviously on the personal homepage of someone at UCLA with the local login name "tao" (the form of the URL is a dead giveaway for that). So what do you think happens to this link if that person some day moves to another university (or retires), and his user account on UCLA's servers gets deleted?
May
14
comment Prove that $\partial A$ is a cutset of connected $X$ if $\operatorname{Int}(A)$ and $\operatorname{Int}(X - A)$ are nonempty
Hint: $\partial A = \partial(X-A)$
May
6
comment Probability of winning the lottery the more you play it?
"If you play once, you have a 50% chance of winning. If you play twice, you have doubled your chance of winning it once." So if I play twice, I have a chance of $2\times 50\% = 100\%$ of winning? That doesn't seem right.
May
6
comment Simplest proof that some number is transcendental?
Transcendental numbers are "more common" than algebraic numbers, because almost all numbers are transcendental. That's because there are only countably many algebraic numbers, but uncountably many reals.
May
6
comment How to determine whether a polytope is self-tessellating?
One obvious way to create self-tessellating objects of higher dimension is extrusion of self-tessellating objects of lower dimension.
May
4
comment How to prove $\mathcal{L}^2[(0,1)]$ is a Hilbert Space
Can you please give an explicit example for the non-positive definiteness of the inner product?
May
3
comment Discrete math of $i^3$
@Uncountable: There's some irony in someone with that username suggesting the use of induction. :-)
May
3
comment Can we have a one-one function from [0,1] to the set of irrational numbers?
@user21820: What exactly do you think I have to justify? That $\pi$ is transcendental is a well-known fact; see e.g. Wikipedia.
May
2
comment Is $f:\mathbb{Q^*} \rightarrow \mathbb{Q}$ by $f(\frac{a}{b}) = \frac{\max{(a,b)}}{\min{(a,b)}}$ a function?
What are the possible values of $a$ and $b$? In particular, can $b$ be negative?
May
2
comment Is there fundamental goal of mathematics?
Does this qualify?
May
2
comment Intersection of two sets which are equivalence on set A is always equivalence?
@Sharma: A relation is a set. See my answer.
May
2
comment examples of a special problem in linear transformation
How do you define "distinct"? Does $T=2S$ already count as distinct?
May
2
comment Determinant of a otherwise constant matrix with a constant diagonal
Subtract the second row from the first.
May
2
comment How to prove that $\frac{\ln 12}{\ln 18}$ is irrational witout using the change of base rule?
Anyway, even if you could prove the claim, that would not solve your given task because you'd not use the change of base rule.