Asaf Karagila
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117/100 score
 9s revised Proving Two Sets are Equal - Infinite Sets - Example edited tags 1h revised Evaluating the triple integral $\iiint \limits_R ze^{-(x^2+y^2+z^2)} \, \, dV$ deleted 9 characters in body; edited title 1h comment Definability in $L(\omega_1)$ Well, as for $L(\beta)$ it is the unique transitive structure satisfying some finite fragment of $\sf ZF$ and $V=L$ which has height $\beta$. Of course, $L(\beta)$ itself requires $\beta$ as a parameter in the definition; but internally it might be that all the elements are definable in $L(\beta)$ without parameters. 2h comment Definability in $L(\omega_1)$ What is the formula defining $B$? Does it have parameters? 3h revised What does this $TS \models P$ mean in relation to set theory. edited tags 8h revised Four different green balls and red balls edited tags 9h comment Where does the proof of $\sqrt 2$ is irrational break down when trying to prove the same for $\sqrt 4$? In this particular case, sure. But the first statement against contradiction based proof is much broader than $\sqrt2\notin\Bbb Q$. 9h comment Where does the proof of $\sqrt 2$ is irrational break down when trying to prove the same for $\sqrt 4$? How do you know that your direct proof doesn't have gaps in it? Even if you think you're careful, how can you be sure? But I do agree that we should strive to minimize the proofs by contradiction that we use, if only because those can often pile up and then you lose track of your proof, and sight of the theorem. 9h revised Are locally compact Hausdorff spaces with the homeomorphic one-point compactification necessarily homeomorphic themselves? Hausdorf typo, so I also fixed the title. 9h revised What does it mean for something to hold “up to isomorphism”? edited tags 9h comment Where does the proof of $\sqrt 2$ is irrational break down when trying to prove the same for $\sqrt 4$? @Matthew: Not an integer, sure. Why does that mean it is irrational? 10h awarded Guru 15h revised A 2D smoothing convolution filter edited tags 19h revised show that there is a $\mathbb P$-name $\sigma$ such that $M[G]\vDash \exists x\phi (x) \iff M[G]\vDash \phi (\sigma [G])$ added 77 characters in body 19h answered show that there is a $\mathbb P$-name $\sigma$ such that $M[G]\vDash \exists x\phi (x) \iff M[G]\vDash \phi (\sigma [G])$ 20h comment Does Russel's paradox preclude us from using the power set to generate every possible set? That's a bunch of "I don't want to show other people that I don't understand because I'm afraid to be ridiculed by others. So I expect my teachers to magically show me what I don't understand, in a way that won't embarrass me in front of everyone". I have nothing more to say here, so I won't bother with this thread anymore. But learning involves putting your pride aside and being open and honest about what you know or don't know. If you can't get that through your head, then I do not envy your teachers. Best of luck in your future endeavors. 22h comment Phd In Pure mathematics. meta.math.stackexchange.com/questions/19799/… 22h comment Is $\left\{0,1,2\right\}^{\mathbb{Z}^2}=\left\{\left\{0,1,2\right\}^{\mathbb{Z}}\right\}^{\mathbb{Z}}$? Isomorphic as whatever structure that bijection preserves. :-) 22h revised Is $\left\{0,1,2\right\}^{\mathbb{Z}^2}=\left\{\left\{0,1,2\right\}^{\mathbb{Z}}\right\}^{\mathbb{Z}}$? deleted 2 characters in body 23h comment Is $\left\{0,1,2\right\}^{\mathbb{Z}^2}=\left\{\left\{0,1,2\right\}^{\mathbb{Z}}\right\}^{\mathbb{Z}}$? @Thomas: In linear algebra too. At least that's what she said. :-)