/sci/ - Science & Math

>>8773770
You have a geometric intuition/model for why [math] 1/2 + 1/4 + 1/8 + ... = 1 [/math] should be true and in analysis you learn a theory taylored to make the geometric intuition "true". And then you go on and require all notions of infinite sum follow some intuition of yours.

Just because something is true for the standard math of finite objects doesn't imply it's true for an infinite setting. This is a totally different context.

Consider the claim
>if a set B is bigger than some smaller set S (i.e. |B|>|S|), then the set of all subsets of B, i.e. the power set PB, is bigger than the PS, i.e. |B|>|S| implies |PB|>|PS|).
This is evident for finite sets but unprovable in general (like the continuum hypothesis)

You can write down a theory of infinite sums where the sum of all natural numbers can't be evaluated, and you can write down theories where it's -1/12. And the latter is a value that various seemingly independent theories agree upon. Besides, the theories where the sum equals -1/12 are none that many people learn about (e.g. with sums alla Ramanujan or defined via analytic continuation).

>>8719825
In sympathetic geometry you have a topological manifold and a tensor w - just like with a Riemann space, but the tensor isn't a symmetric metric g.

The simplest example would be, in components, the 2x2 matrix
w = ((0, 1), (-1, 0))
So if in R^2 you consider a vector X := (q, p) as a function of time and the function H = p^2 / (2m) + U(q), then the flow equation

(∂/∂t) X = w · (∂/∂q, ∂/∂p) H
expresses
mv = p
F = -∂/∂q U(q)

So symplectic geometry is the math field where you just look at even-dimensional spaces with w's (and any functions on that space, such as H), and before you know it you derived all the math to be interpreted as of classical mechanics.

>>8335398
All people are capable of being indoctrinated, what you believe in it's a matter whether you're born in Bombay or Dubai or wherever.

Old men wrote down rule books to get power and stabilize, and wherever structure is required, people choose from what's available.

I can't blame anyone - all people are capable of being indoctrinated. But that's not so say you should invite such structures.

If it's not the influx of religions isn't fought enough in the West these days, then because we're only left with economic systems that leave common people with two many options and questions.