/sci/ - Science & Math

Am I the only one who notices a certain resemblance?

>>4128408

well, humans tend to look like each other.

>>4128408
http://cheezburger.com/View/2866765568

lol

anyone else notice like 3/4 of famous mathematicians are frenchfags? whats up with dat?

>>4128420
That's... that's terrible.

>>4128423
Many of them are german and russian (the newer ones) too.

>>4128423
Mathematics developed much more slowly in England because they kept trying to use Newton's less efficient approach to calculus.

France was the most powerful country on the continent for a fairly long period of time, so it only makes sense that most famous mathematicians would be French, although a few of them were German (Hesse and Pfaff come to mind, for example), too.

>>4128423
well not quite so http://en.wikipedia.org/wiki/List_of_mathematicians_(A) and next pages

>>4128432
Some people also changed their name to fit in with all the French-ness. Take Giuseppe Lagrangia, whom you might know better as Lagrange.

First problem:
\left \lim_{ x\to0\0 }x \left[ \frac{1}{x}\right\rfloor
where \left[ \frac{1}{x} \right] is floor function.

>>4128450
wat

>>4128450
In other words when x->0 determine limit of x[1/x], where [1/x] stands for floor function

>>4128475
>>4128475
multiply x into the function and cancel out the x's amirite?

>>4128450
>>4128469
Im not used to use tex. I prefer old school pen&paper mathematics

>>4128490
No. If you look closely you'll see that it's indeterminate symbol.

>>4128497
enjoy writing your thesis in pen.

>>4128475
x[1/x] < 1. x[1/x] > x/(x+1) -> 1 as x->0
So the limit is 1.

>>4128520
Correct.

>>4128537
>>4128401
Btw if ya'll got some analysis problems feel free to post.

>>4128401
Determine limit of given sequence:
a(n)=((2^n)/(n!)), n->infinity

>>4128450

<div class="math">\lim_{x \to 0}\left\lfloor\frac{1}{x}\right\rfloor</div>

>>4128570
How do I? I didn't even...

>>4128569
0. Google "Stirling's approximation." Also delete your thread.

>>4128569

<div class="math">\lim_{n \to \infty}\left(a_{n}=\frac{2^{n}}{n!}\right)</div>

analysis is for faggots & masochist

>>4128590
lim n->inf (a(n+1)/an) = lim n-> inf((n!/(n+1)!)*(2^(n+1)/2^n))= lim n->inf((1/(n+1))*2)=0 => lim n->inf (an) = 0
Just did your homework >:

>>4128632
Hi, I'm a foreigner, what's the difference between Calculus and Analysi?

>>4128673
Same question answer plz

>>4128423
It's an an early development of analysis thing. When I did a course on it, the lecturer even made up the acronym FMOTNC (French Mathematician Of The Nineteenth Century) to introduce them all.

>>4128692

I think the difference is analysis is rigorous math faggotry while calculus is like learning the results from analysis and how to use them to solve problems in other fields.

>>4128673
>>4128692
Calculus is just the analysis of differentiable functions, or integrable ones. Analysis can cover much less 'nice' structures than differentiable ones. For example, measure theory is analysis but most measurable functions are not differentiable

>>4128721
no, that is not the difference you humongous faggot. the calculus you're talking about is the freshman engineer's version of, "derp herp, how do I solve problem, let me use plug and chug equation devised by a physicist or mathematician!"

>>4128673
I think that the difference bettwen "calculus" and "analysis" is that calculus=basic algebra (solving simple equations, inequalities, simplyfing etc.) and that analysis is harder. However I'm foreigner too so its possible that I'm wrong.

analysis doesn't care about numerical values.
Calculus does.

analysis huh?
Show that the sum of 1/p over all prime numbers p diverges

The actual difference between analysis and calculus:
calculus is an area of math that solves specific types of problems
Analysis is one of the three main "methods" in math, the other two being algebra and geometry/topology. Analysis consists of those mathematical techniques that concern "infinities". For example, if you were asked to find the area of a triangle, you could solve it the geometric/algebraic way (base * height / 2) or the analysis way (integrals). Thus, analysis consists of a lot more than just "more rigorous calculus". It composes about half of number theory, arguably point set topology, and a shitload of other stuff.

What's the weak closure of C(R) (continuous functions over the reals)?

I actually don't know this one. It's not just the pointwise limits of continuous functions since R^R is not first countable. Maybe it's all measurable functions...

>>4129968
And I mean closure in R^R (under the product topology).

let S = √(1 + √(2 + √(3 + ...)))
(a) show S converges
(b) find what S converges to

>>4130041
converges to the "nested radical constant"

>implying the best mathematician of all time wasn't german (gauss)
>implying the second best mathematician of all time wasn't swedish (euler)

>>4128520
>>4128537

But x/(x+1) -> 0 as x->0.

>>4130073
>ordering mathematicians
>probably doesn't even know any modern mathematicians other than Wiles and Perelman