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1h
comment What is an affine space?
@Stan: I've made an edit. (do you get pinged when I edit my post?)
1h
revised What is an affine space?
added 1783 characters in body
12h
answered Is there such thing as an unnormed vector space?
13h
answered What is an affine space?
16h
answered Basic Set Theory regarding the set $\{0\}$
21h
revised Is the simplest form of a quadratic equation factored form or standard form?
added 221 characters in body
21h
revised Is the simplest form of a quadratic equation factored form or standard form?
added 221 characters in body
21h
revised Is the simplest form of a quadratic equation factored form or standard form?
added 156 characters in body
22h
answered Is the simplest form of a quadratic equation factored form or standard form?
1d
comment Determinant: Alternative Definition (Matrices)
If you're comfortable with group theory and the classical groups, I believe that the multiplicative group of nonzero scalars is (isomorphic to) the abelianization of $GL(V)$, the group of invertible endomorphisms. The map from $GL(V)$ to its abelianization is canonical, and the isomorphism with the nonzero scalars is the determinant. (there's probably a natural way to single out the determinant specifically rather than any of the other possible isomorphisms...)
1d
answered Is Relativity a specific instance of Riemannian geometry?
1d
answered Contradictory definition in set theory book?
2d
comment Polynomials: functions of functions integer roots
Go ahead.......
2d
comment Polynomials: functions of functions integer roots
What you wrote doesn't make much sense: did you mean something like "Define functions $f_m$ by the recursion relation $f_1(x) = f(x)$ and $f_k(x) = f(f_{k-1}(x))$. Prove, for all $m > 0$, there is no $x \in \mathbf{Z}$ such that $f_m(x) = x$, except for $x=1$."?
2d
comment Random Variables that aren't measurable
Please do not make your font size twice as big as everything else.
2d
revised Random Variables that aren't measurable
Removed obnoxious font size
2d
comment Proof that this differential form is not exact
In $\int_{S^1} x \, \mathrm{d}y$, $x$ is not a constant, so you can't factor it out.
2d
comment The “Empty Tuple” or “0-Tuple”: Its Definition and Properties
Are you sure you want $S^0 \times S^n = S^n$? I'm pretty sure other similar examples already fail, such as $S^2 \times S^2 \neq S^4$.
Dec
17
comment Understanding infinity
@user: One thing that often fails to reach the layperson is that there are at least two very different kinds of infinite things mathematicians study: on the one hand, various infinite cardinals describe the "size" (or "complexity") of a set. On the other hand, infinity acts more like a place in more geometric contexts, such as the two extended real numbers $\pm \infty$ you see in calculus. These two notions really don't relate to each other at all.
Dec
17
comment Understanding infinity
... much like the number 1.