Is everything just algebra?

everything thing in life can be solved with proportions

>>8499649
Nah, some things are arithmetic

>>8499654
>I'm a rationalist

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All the higher maths I've looked at are all just novel applications of Algebra.

Is this all there is?

Wouldn't the basics of calculus be considered fundamentally different from algebra? It involves dealing with the infinite and the infinitesimal.

>>8499681
Limits and derivatives are some of the most basic applications in calculus, and they are expressed algebraically.

>>8499681
https://en.m.wikipedia.org/wiki/Differential_algebra

>>8499686
So is it just doing algebra with differentials, as opposed to with numbers?

i.e.

f(x, y) = x^4 + y^3 + (xy)^2 + y

to

f(dz/dx, dy/dx) = (dz/dx)^4 + (dy/dx)^3 + (dy/dx * dz/dx)^2 + dy/dx

>>8499681
No. Infinitesimals are very natural in algebra. Just look at rings of the form R[x]/<x^2> .

>>8499736
what's a ring?

>>8499750
https://en.wikipedia.org/wiki/Ring_(mathematics)

>>8499753
sweet. thanks

I think the point at which "algebra" begins to falter is when things stop adhering to a manageable set of rules. Stuff with big ugly generating sets, stuff with big ugly presentations, stuff with fuzzy truth values, and stuff in which the rules change dynamically. Fortunately for our dear friend algebra, a large part of mathematics is centred on foundational principles. Math was created to handle problems which behave according to hard logical manipulation, so in a sense this other stuff embodies mathematics moving out of its comfort zone (all for the better, I think).

tl;dr Most of mathematics can be founded algebraically, but the more exotic stuff needs more exotic tools.

>>8499736
I'm a babb, is this the factor group of the set of polynomials on R over x^2?

>>8499649
No, some things are analysis.

>>8499685
>>8499686
>>8499736
Undergrads detected.

>>8499794
>I'm a babb, is this the factor group of the set of polynomials on R over x^2?

The way to think about it is as elements a+bx where a,b in R and x^2=0.

>>8499796
>Undergrads detected.
Nope

>>8499805
Ah yeah, high school was fun.

>Fundamental theorem of algebra
>No purely algebraic proof
Algebraists BTFO

>>8499824
Yes there is.

Pf:

- Define C as the algebraic closure of R.
- Claim is true by definition.

QED

>>8499840
Can you prove there exists a set that is a closure?

Also
> pure algebraic
> R

i choose to believe everything is algebra because if everything was topology i would fucking kill myself

>>8499854
>Can you prove there exists a set that is a closure?

What a stupid fucking question. All it means is every integer polynomial has symbols which let you reduce it to degree 1 polynomials, and that every polynomial has as many nonunique zeroes as its degree. You can define anything to have that property and you're fine, you don't need to say anything about the symbols themselves, it's just not as useful a perspective.

>>8500393


An algebra is any story whose presupposition about its existence can be used to find itself by comparing it to itself. It is a tautology x = y that a priori assumes itself exists x = x.
Since different things exist, then different stories (algebras) can be related by the story of their stories (topologies, combinatorics, categories, etc) if you are extremely careful (rigorous) with whether those stories are useful to be believed, and you never assume you can know all of the stories (algebras). That is why algebra is not everything.

>>8500440
No, an algebra is module M together with a bilinear map M x M --> M.

What's linear algebra?

>>8500571
A vector space over a field.

>>8500571
Algebra with lines.

>>8500577
>not a module over a ring
fucking haram

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>>8499649
What does this mean for me if I got a C- in all of my algebra courses?

>>8500836
You can't be a mathematician.

>>8499649

Even better, everything is category theory.