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bio website thomasoandrews.com
location Cambridge, MA
age 48
visits member for 3 years, 4 months
seen 2 hours ago

Refund? Refund?!?

I've read the proof. I still think it is inconceivable that exponentiation is Diophantine.


2h
comment Soft Question: Idea behind complete orthogonal system
Sorry, I'm finding it very hard to come up with a good answer. It really does feel like it needs a good intro book.
4h
comment Soft Question: Idea behind complete orthogonal system
I suspect these terms are a bit much for a question here - the full answers and definitions are really the beginning chapters of a book. But I'll try to write a short version.
4h
comment Soft Question: Idea behind complete orthogonal system
It also includes $<f_n,f_m>=0$ for $n\neq m$. That's the "ortho" part, meaning "orthogonal" or "right angle." $<f_n,f_n>=1$ is the "normal" part. "Normal" is often left out, because it is easy to take a orthogonal basis and make it orthonormal...
4h
comment Soft Question: Idea behind complete orthogonal system
Do you know what an "orthonormal basis" means in $n$-dimensional vector spaces?
4h
comment Soft Question: Idea behind complete orthogonal system
Finally, please tell us what else you know. How much linear algebra do you know, for example?
4h
comment Soft Question: Idea behind complete orthogonal system
In (2), what do you mean by "at integer jumps?" And do you mean the set of all such functions? A single function cannot be a complete orthonormal basis of any set of functions other than the one-dimensional one containing it.
4h
comment Soft Question: Idea behind complete orthogonal system
Just curious, how are you learning these terms without learning what they mean? Whatever book or resource you are using should define then, I'd hope...
4h
revised Soft Question: Idea behind complete orthogonal system
edited tags
6h
comment Alternative proof for the fact that a continuous function on a closed interval attains its boundaries.
Yes, I meant $f(x)<M$. This proof shows that, for any strict upper bound, we can find a lower upper bound.
6h
comment What's the name of this algebraic property?
@Semiclassical No, you misread my comment. The rationals are closed under subtraction. That is what the above says...
6h
comment What's the name of this algebraic property?
This can be written as: $S$ is closed under subtraction. That is, if $a,b\in S$ and $a-b$ exists, then $a-b\in S$.
7h
comment Do all primes $p$ except 2 and 3 divide the sum of the squares of integers from 0 to $p - 1$?
And the condition that $p$ is prime, of course...
7h
comment Alternative proof for the fact that a continuous function on a closed interval attains its boundaries.
$g$ is obviously continuous, if $g(x)<M$ for all $x\in[a,b]$.
7h
revised For any positive integer $n$, let $f_n:[0,1] \to\mathbb R$ be defined by $f_n(x)=\frac x{nx+1}$ for $x \in [0,1]$.
added 48 characters in body; edited title; edited tags
8h
comment Very simple notation question
Are you talking only about "base $10$ decomposition," or are you including, say, $11=1+2+3+5$?
9h
answered Atiyah-Macdonald 2.3
9h
comment Atiyah-Macdonald 2.3
Is that really viewing $P$ as a $k$-module? Seems like it is treating $P\otimes k$ as a $k$-module.
1d
comment Why, or why not, is $5^{log_3(n)} \in \mathcal{O}(n^2)$?
$\alpha = \log_3 5$. Much easier to avoid natural logs and write: $5=3^{\log_3 5}$ so $5^{n} = n^{\log_3 5}$...
1d
comment Is my proof about $\liminf$ of bounded real sequences correct?
You didn't say it, and you could have, so it was confusing. You used $N-\epsilon$ in an odd way, did not highlight it, and did not put that condition on $N$. The letters $N-\epsilon$ don't imply the other fact - you still have to state it.
1d
comment combination of quadratic and cubic series
Not really a hint :)