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>> No.11164160 [View]
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11164160

Suppose [math]A[/math] is a closed subspace [math]C(S)[/math], where [math]S[/math] is a compact Hausdorff space; suppose [math]\mu[/math] is an extreme point of the unit ball of [math]A^{\perp}[/math]; and suppose [math]f\in C(S)[/math] is a real function such that [math]\displaystyle \int_{S}gf d\mu =0[/math] for every [math]g\in A[/math]. Prove that [math]f[/math] is constant on the support of [math]\mu[/math]. Show, by an example, that the conclusion is false if the word "real" is omitted from the hypotheses.

>> No.10013822 [View]
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10013822

>>10013815
Definitions are not proof.

Prove it.

>> No.9892075 [View]
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9892075

>>9889074
If there exists a number close enough to infinity to be considered infinity, then there also exists a 0.999... value close enough to 1 to be considered 1.

Pretty sure there isn't a number close to infinity though.

>> No.9772396 [View]
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9772396

>>9772059
>do{
>x+=1;
>}while(x<10);

>while(x<10){
>x+=1;
>}

>DOing anything ever

>> No.9749573 [View]
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9749573

>>9749551
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3182557/
https://www.ncbi.nlm.nih.gov/pubmed/23919982
https://www.ncbi.nlm.nih.gov/pubmed/23722424
http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0100248
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2889158/
https://www.ncbi.nlm.nih.gov/pubmed/23358157
http://www.pnas.org/content/pnas/111/42/15273.full.pdf
http://www.ipr.northwestern.edu/publications/docs/workingpapers/2013/IPR-WP-13-09.pdf
https://helda.helsinki.fi/bitstream/handle/10138/38881/HECER_DP364.pdf
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3907681/
https://www.sciencedirect.com/science/article/pii/S016028961500135X
https://www.ncbi.nlm.nih.gov/pubmed/23358156
https://www.sciencedirect.com/science/article/pii/S0160289614000178

>> No.9733472 [View]
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9733472

>>9733467
>0.888... + 0.111... = 1
>8 + 1 = 9
Choose one.

>> No.9726447 [View]
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9726447

>>9726436
>dead ancient people can't be wrong.
gr8 defense m8

>> No.9641466 [View]
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9641466

How did they know there was no air in space

How did they know there was no air on the moon

You only need a scuba suit when you're underwater

>> No.9615514 [View]
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9615514

Okay infininiggers
If you're so smart, solve this problem:
Construct ∞ without invoking the words "infinity" or "infinite" or any related word or term derived from them, and you may also not use the symbol ∞ outside of your conclusion.
Show all your work, be thorough.

>> No.9602584 [View]
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9602584

>translating gookanese into any non-garbage language
fuckin lies

>> No.9564370 [View]
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9564370

>>9564286
Base 10
8/9 > 0.888...
9/9 > 0.999...

Base 11
9/a > 0.999...
a/a > 0.aaa...

Base 12
9/b > 0.999...

[math]0.\bar{9}_{base10} < 0.\bar{a}_{base11} < 0.\bar{b}_{base12}[/math]
Or
[math]0.\bar{b}_{base10} = \mathbb{FUCK}[/math]
http://www.wolframalpha.com/input/?i=0.b...++to+base+10

>> No.9542761 [View]
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9542761

>>9542755
Vector is not a space. Its a fucking word.

>> No.9540440 [View]
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9540440

>axiom
What a fucking shitty buzzword.

>> No.9526909 [View]
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9526909

You have 10 minutes to prove that melanin overdose doesn't cause brain damage.

>> No.9497369 [View]
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9497369

>>9497362
The only infinite amount that will ever matter for you is the eternity of hell.

>> No.9469223 [View]
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9469223

>>9469201
And they also have a finite fraction representation :^)

[math]\frac{9}{10^n}[/math] is the same as [math]\frac{\big[ 9 \big]...}{1 \big[ 0 \big]...} = \frac{99...}{100...} = \frac{999...}{1000...} = \frac{9999...}{10000...} ... [/math] and so on. To evaluate the decimal number [math]0.\bar{9}[/math] is to simultaneously evaluate the fraction [math]\frac{\bar{9}}{1\bar{0}}[/math], where any finite test of countability in the 9's and 0's, even after an infinite amount of finite tests, will always produce a number [math]\frac{x}{y}[/math] where x < y and thus not equal to 1.

>> No.9425647 [DELETED]  [View]
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9425647

>read textbook a head of time before classes start
>help brainlets who are confused whit the lectures
>"Wow anon! You must be a Senior"

>> No.9397957 [View]
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9397957

>>9397947
[math]\frac{JewsKilledJesus}{JesusWasSemitic} \approx JewsAreAntisemites[/math]

>> No.9396102 [DELETED]  [View]
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9396102

[math]\infty[/math] is not a number
[math]n \rightarrow \infty[/math] cannot evaluate to a finite answer in finite time
[math]0.\bar{9} < 1.0[/math]
[math]0 \neq 0.\bar{0}1 \ngeq 0.\bar{1}_{base2} \ngeq 0.\bar{9}_{base10} \ngeq 0.\bar{F}_{base16} \neq 1.0[/math]
[math]N \geq 2 \rightarrow \infty; (0.\overline{N-1}_{baseN} < 0.\overline{N}_{base(N+1)})[/math]
[math]X = \sum{N/3=1}^{/infty} 0.(\frac{N}{3})_{baseN} × 3_{base10} = 1.0 \neq 0.\bar{9}[/math]
[math]0.\overline{N-1}_{baseN} = [/math] NaN

>> No.9396099 [DELETED]  [View]
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9396099

[math]\infty[/math] is not a number
[math]n \rightarrow \infty[/math] cannot evaluate to a finite answer in finite time
[math]0.\bar{9} < 1.0[/math]
[math]0 \neq 0.\bar{0}1 \ngeq 0.\bar{1}_{base2} \ngeq 0.\bar{9}_{base10} \ngeq 0.\bar{F}_{base16} \neq 1.0[/math]
[math]N \geq 2 \rightarrow \infty; (0.\overline{N-1}_{baseN} < 0.\overline{N}_{base(N+1)})[/math]
[math]X = \sum{N%3=0}^{/infty} 0.(\frac{N}{3})_{baseN} × 3_{base10} = 1.0 \neq 0.\bar{9}[/math]
[math]0.\overline{N-1}_{baseN} = [/math] NaN

>> No.9389653 [View]
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9389653

>>9389647
>racial egalitarian "skeptic" makes cringe-tier jokes after getting btfo

I'm almost positive you wear a fedora.

>> No.9387545 [View]
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9387545

>>9387540
If a tree falls in a forest and nothing is around to hear it, does it make a sound?

>> No.9382667 [View]
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9382667

>>9379624
Cause you are retarded.

>> No.9371554 [View]
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9371554

>>9371549
The winner decides the course of history.



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