/sci/ - Science & Math

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.

>>10013815
Definitions are not proof.

Prove it.

>>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.

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

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

>DOing anything ever

>>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

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

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

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

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.

>translating gookanese into any non-garbage language
fuckin lies

>>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

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

>axiom
What a fucking shitty buzzword.

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

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

>>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.

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

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

[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

[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

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

I'm almost positive you wear a fedora.

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

>>9379624
Cause you are retarded.

>>9371549
The winner decides the course of history.