/sci/ - Science & Math

1. Euclid
2. Riemann
3. Cartan
4. Gauss

hello

"Hiervon wäre allerdings ein strenger Beweis zu wünschen; ich habe indess die Aufsuchung desselben nach einegen flüchtigen vergeblichen Versuchen vorläufig bei Seite gelassen, da er für den nächsten Zweck meiner Untersuchung entbehrlich schien."

Is this the greatest cop-out of all time, or is it an acceptable admission of limitations?

Sup guys.

I'm a graduate student in computer science.

One of my teachers said this, during type theory course:
There is no confluence in the Integral Calculus.

I can imagine why and I can wait until monday to ask my teacher directly.
But If someone already know... I'm listening.

<span class="math">\frac{\sqrt{1842603-690 \sqrt{5831385}}}{60}[/spoiler]

<span class="math">e^{ \pi } - \pi[/spoiler]

<span class="math">\pi^2 + \frac{\pi}{24}[/spoiler]

<span class="math">\sin(11)[/spoiler]

<span class="math">\cos(\ln( \pi + 20))[/spoiler]

<span class="math">2cos(cos(cos(cos(cos(cos(cos5))))))^{2}[/spoiler]

<span class="math">e^{6} - \pi^{4} - \pi^{5}[/spoiler]

<span class="math">\frac{\pi^{9}}{e^{8}}[/spoiler]

<span class="math">\pi e^{\frac{1}{\pi} \cdot \int_{0}^{1} \arctan{\frac{4 \pi t - 4 \pi t^{2} {\rm{artanh}} t}}{3\pi^{2} t^{2} + 4t^{2} {\rm{artanh}} t} - 8t {\rm{artanh}} t} +4}} \frac{dt}{t}}[/spoiler]

How does one find the correct stoichiometry of reactions without trial and error?

example:
Cr2O3 + Na2CO3 + KNO3 --> Na2Cr2O4 + CO2 + KNO2

Which of these curves is the longest?

g1: [0,1] -> R, x -> 3x^2

g2: [0,1] -> R, x -> 2x^6

g3: [0,1] -> R, x -> x^4

Now, to calculate each individual length I would insert each funtion into:

L0,1=int( sqrt( 1+(g')^2 )) from 0 to 1

Trouble is, integrating the functions by hand is a mess and during a test I don't have the time nor the possibility to use a calculator or similar.
Is there a quicker way to find out which answer meats the criteria?

Can you believe some med student stole my fucking idea?

Ok, this has been bothering me for a while now. The Riemann integral is defined as:

<span class="math"> \int_{a}^{b}f(x)\mathrm{d}x=\lim_{\left \| P \right \|\rightarrow 0}\sum_{k=1}^{n}f(x_i^*)(x_i-x_{i-1}) [/spoiler]

Where <span class="math"> P=\left \{ a=x_0<\cdots<x_n=b \right \} [/spoiler], <span class="math"> x_i^*\in[x_{i-1},x_i] [/spoiler], and <span class="math"> \left \| P \right \| [/spoiler] is the mesh of the partition <span class="math"> P [/spoiler]. My question is, how do we use this to prove:

<span class="math"> \int_{a}^{a}f(x)\mathrm{d}x=0 [/spoiler]

I guess my real problem here is how you're supposed to define a partition of the interval <span class="math"> [a,a] [/spoiler]. I figured maybe it's defined as <span class="math"> P=\left \{ a,\cdots,a \right \} [/spoiler], but I can't seem to find anything about this online.

Well I'll just leave this here...
http://arxiv.org/ftp/arxiv/papers/1006/1006.0381.pdf

>>1385023

Yeah, we've met. My foot, meet your ass.

LESS FILLING
MORE MEAT

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65...

>Q: Why can't parallel lines intersect?
>A: Because we are using a Euclidean metric