Reputation
Top tag
Next privilege 1,000 Rep.
Create new tags
Badges
1 5 20
Newest
 Organizer
Impact
~11k people reached

21h
comment Is there any relatively quick way to diagonalize this matrix with an orthogonal matrix?
Yeah, sorry. I calculated the eigenvalues twice in my notebook and copied the wrong ones down.
21h
comment Investigation Problem to challenge mathematical reasoning
I don't know how "original" you need to be but this MO post mathoverflow.net/questions/48771/… seems to be related. Some of the proofs are a little above Calc 2, but you may be able to understand the first example: Euler's (not Euclid's) proof that their are infinitely primes.
22h
comment Is there any relatively quick way to diagonalize this matrix with an orthogonal matrix?
I learned orthogonal as $A\cdot A^{T} = I_n$ and I wasn't really aware of the orthonormality that needed preservation. Normalizing each vector gives an identity matrix. Thanks!
2d
comment Showing $A+B$ is invertible?
Thanks. I guess I should have kept trying... At least I was on the right track after all. :)
Apr
27
comment How to derive this identity: $\lim _{x\to \infty} (1 + f(x))^{\frac{1}{g(x)}} = \mathrm e^{\lim_{x \to \infty} \frac{f(x)}{g(x)}}$
If $f(x)=1$ and $g(x)=1$ then the LHS goes to $2$ and the RHS goes to $e$... I don't think this is true in general.
Apr
27
comment Necessity of Differential Forms
Not entirely an answer to your question (it doesn't answer the importance in analysis) but for a more intuitive explanation, Tao gives an introduction to differential forms here: math.ucla.edu/~tao/preprints/forms.pdf and argues the algebraic laws of the differential forms derive from a roughly speaking more intuitive, what I would describe as: "infinitesimal geometry".
Apr
22
comment f(x) is a function such that $\lim_{x\to0} f(x)/x=1$
You really shouldn't assume $f(x)$ is $\sin(x)$ because you have not shown that $a$ and $b$ are unique and irrespective of $f(x)$.
Mar
17
comment Terry Tao, Russells Paradox, definition of a set
Although it is related to lazy evaluation, I believe (although I could be wrong), as EJP has mentioned, short circuiting is a better term to describe this. The main reason being that lazy evaluation is much larger in scope and has further applications beyond this example. It refers to not computing values until they are needed, whereas short circuiting specifically refers to not computing values because they are unneeded.
Feb
23
comment Prove that zero multiplied by zero is equal to zero.
@ruakh: Oh yes, that's probably it: I'm thinking of fields.
Feb
23
comment Prove that zero multiplied by zero is equal to zero.
Huh, usually I have had to derive this. Although maybe it depends on what you take for granted... $a \cdot 0 = 0$ but $0 + 0 = 0$ therefore, $a \cdot 0 = a \cdot ( 0 + 0 ) = a \cdot 0 + a \cdot 0$. So $a \cdot 0 = a \cdot 0 + a \cdot 0 \implies 0 = a \cdot 0$
Feb
16
comment Prove that $\int_{0}^{\infty} \sin(t^2)\,dt$ equals $\sqrt{\pi/8}$
The top one is one of the two Fresnel integrals. wikiwand.com/en/Fresnel_integral The specific problem is mentioned later in the wikipedia page.
Feb
11
comment Proving trefoil group is isomorphic to a fundamental group.
It think so, it can now be shown that $x_1 = b^2a^-1$ and that $x_2 = ab^{-1}$, so $a$, $b$ also generates the trefoil group, therefore we have an alternative presentation, and the two groups must be isomorphic.
Oct
31
comment Confused about basics of subsequences
You do realize this is a sequence and not a series? I once confused the two and I sense that maybe you are confusing the two...
Oct
26
comment Mathematical texts: white background or tan
I don't really have a problem with white colored background. I would guess, that it's just easier to get a hold of white colored paper since it is "more standard." Not so much math but I feel like at least some of the paper writing formats (MLA, APA, Chicago etc.) require white as the color of choice. There would be less contrast between the black font and tan which may make it hard for people with poor vision to read. Just ask the professor. (This is ALL ENTIRELY speculative and a very unsupported guess, more of something to consider).
Oct
25
comment Give a regular expression that generates C.
This is off topic but I have never seen a language use (in particular) the #. Usually it is something like: /* and */
Oct
12
comment Neighbors of Irrational Numbers on Real Number Line
Maybe this can help convince you otherwise: wikiwand.com/en/Archimedean_property Instead of arguing about what infinitesimal neighbor 0 has, the Archimedean property indicates that over $\mathbb{R}$ there exists no infinitesimal objects in the first place. Hence, the "next neighbor" is neither rational nor irrational as it doesn't exist.
Oct
9
comment Relationship between perfect squares and infinite series (zeta function)
I don't believe there is any nice formula: wikiwand.com/en/Ap%C3%A9ry%27s_constant
Sep
29
comment Mathematical Symbols
Possible duplicate: xkcd.com/927
Sep
29
comment Help with verifying integral inequality.
@mercio: Plugging in the linear transformation $t$ gives an equality for the first statement. So then looking at the comment above you can use this fact to conclude: $\int_x^1 f(t) dt \geq \int_x^1 t dt$. Therefore: $$\left|\int_0^1 f(x)dx \right|^2 \geq \int_0^1 x dx \cdot \int_0^1 x dx$$ and similarly from the Cauchy-Schwarz inequality: $$\int_0^1 |f(x)|^2 dx = \int_0^1 x f(x) dx$$
Sep
29
comment Help with verifying integral inequality.
@Aravind: Sorry, but do you mind clarifying why we cannot conclude thusly?