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9s
revised Proving Two Sets are Equal - Infinite Sets - Example
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1h
revised Evaluating the triple integral $\iiint \limits_R ze^{-(x^2+y^2+z^2)} \, \, dV$
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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.
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8h
revised Four different green balls and red balls
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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”?
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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
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15h
revised A 2D smoothing convolution filter
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19h
revised show that there is a $\mathbb P$-name $\sigma$ such that $M[G]\vDash \exists x\phi (x) \iff M[G]\vDash \phi (\sigma [G])$
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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 $\left\{0,1,2\right\}^{\mathbb{Z}^2}=\left\{\left\{0,1,2\right\}^{\mathbb{Z}}\right\}^{\mathbb{Z}}$?
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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. :-)