Reputation
11,831
Top tag
Next privilege 15,000 Rep.
Protect questions
Badges
2 23 50
Impact
~234k people reached

May
14
revised If $ab=ba$, Prove $a^2$ commutes with $b^2$
added 295 characters in body
May
14
answered If $ab=ba$, Prove $a^2$ commutes with $b^2$
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
13
awarded  Good Answer
May
13
awarded  Nice Answer
May
12
answered Is an irrational number odd or even?
May
12
answered How to Formulate this Linear Algebra Fact in a Coordinate Free way?
May
9
answered Turing Machine Halting problem
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
4
answered $\langle A,B\rangle = \operatorname{tr}(B^*A)$
May
3
answered If $ f $ is injective and $ g $ is injective, then $ f \circ g $ is surjective.
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
3
answered Can we have a one-one function from [0,1] to the set of irrational numbers?
May
2
awarded  Vox Populi
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?