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May
18 |
awarded | Popular Question |
Mar
31 |
awarded | Nice Answer |
Feb
18 |
awarded | Nice Answer |
Feb
21 |
awarded | Yearling |
Jan
14 |
awarded | Nice Answer |
Feb
22 |
awarded | Yearling |
Dec
6 |
answered | Is it consistent with ZFC that for all ordinals $\alpha, \beta < \omega$ it holds that $2^{\aleph_\alpha} = 2^{\aleph_\beta}$? |
Oct
14 |
comment |
Most 'unintuitive' application of the Axiom of Choice?
Resurrecting an old answer here: It should be noted that many of these can be ruled out by resorting to countable AC or dependent choice, which avoid many of the strange consequences of full AC. For example, "A set can be infinite, but have no countably infinite subset", is ruled out by countable AC. |
Oct
14 |
revised |
When $2^\alpha = 2^\beta$ implies $\alpha=\beta$ ($\alpha,\beta$ cardinals)
struck erroneous statements |
Aug
24 |
comment |
Mathematics as a hobby
"Everything else, like getting the books and papers you need, is basically solved by knowing google and wikipedia :-)" How are you seeing the papers? One does need a good university library nearby, for that at the very least. Even MathSciNet isn't available to the general public. |
Aug
22 |
awarded | Nice Answer |
May
8 |
awarded | Civic Duty |
Apr
19 |
awarded | Necromancer |
Mar
13 |
comment |
How do we know that P != LINSPACE without knowing if one is a subset of the other?
That's not a problem. The whole argument is proof by contradiction; you've just provided a different contradiction. |
Mar
13 |
comment |
Is a space with no covering spaces simply connected?
Nitpick: I assume you mean "connected covering space", because otherwise... |
Feb
22 |
awarded | Yearling |
Feb
10 |
comment |
Is the “closedness of the image of operator” needed in the defintion of Fredholm operators?
That "im T + C^n" is supposed to be at the end of the first paragraph. Not sure why it didn't show up there. |
Feb
10 |
answered | Is the “closedness of the image of operator” needed in the defintion of Fredholm operators? |
Dec
14 |
comment |
Proofs that require fundamentally new ways of thinking
I took the last set theory course that Cohen taught, and this isn't how he presented his insight at all (though his book takes this approach). The central problem is "how do I prove that non-constructible [sub]sets [of N] are possible without access to one?", and his solution is "don't use a set; use an adaptive oracle". Once that idea is present, the general method falls right into place. The oracle's set of states can be any partial order, generic filters fall right out, names are clearly necessary, everything else is technical. The hardest part is believing it will actually work. |
Nov
16 |
comment |
Adding a formal inverse of an element to a free monoid
My guess is that adjoining $z^{-1}$ does not get you all the way to $F_2$, but it's not a very well-informed guess. |