/sci/ - Science & Math

[Anonymous No.7060463]

What's the most well accepted elementary mathematics text out there? For something as deep and complex as mathematics there's gotta be some well defined, agreed upon collection of information that completely details the bare essentials and foundations of our mathematics system, going as far back as defining exactly what a number is, exactly how all the mathematical operations we use work and are defined, defining fractions, decimals, arithmetic, etc... all of our mathematical knowledge up to the beginnings of algebra.

I'd love to read this text because throughout my K-12 education I was just kinda told "addition is combining 2 numbers, subtraction is the difference between 2 numbers, etc..." and I didn't think too much about it. But now that I'm in my 3rd semester of calculus I've had a decent amount of exposure to things like proofs, and working with general forms of equations so I've come to appreciate the well-defined structure of later mathematics, so I kinda want to go back and look at a stringent definition of all mathematics, starting from the bare essentials.

[Anonymous No.7060491]

>>7060463
> For something as deep and complex as mathematics there's gotta be some well defined, agreed upon collection of information that completely details the bare essentials and foundations of our mathematics system, going as far back as defining exactly what a number is, exactly how all the mathematical operations we use work and are defined, defining fractions, decimals, arithmetic, etc... all of our mathematical knowledge up to the beginnings of algebra.
there isn't.
get over it.

[Anonymous No.7060544]

Complete formalizations are usually not particularly readable.
There are many libraries, the biggest being Mizar (a more or less dead project now)
http://en.wikipedia.org/wiki/Mizar_system
But to interpret the syntax you'll heave to study some first-order logic.
You shouldn't read Mizar or any other formal library, but learning logic is great, of course.
Here is a fairly comprehensive literature overview to introductory logic:
http://www.logicmatters.net/resources/pdfs/TeachYourselfLogic2015.pdf

>well accepted elementary
Given you understand the language, some direct axiomatizations, e.g. of the theory of groups or rings, is extremely well understood and has numbers as a 'model'. Same with natural numbers and arithmetic (google Peano arithmetic). But then again, foundational math, trying to set up an encompassing framework, will redefine (or model) the idea of groups, ring or numbers.
Just do some logic and that will make sense.

That being said, the philosophy behind the foundations of mathematics, and the many approaches to it, are very very very far from being agreed upon.
Working mathematicans are mostly agnostic and accept the set theory written down in first order logic foundational framework, which established itself around 100 years ago.

>decimals
Decimals come pretty late, from the above perspective. Computational matters, or questions of representation, are generally often treated as an orthogonal subject. Extremely related, but somewhat of a subject of its own.

[Anonymous No.7062079]

>>7060463
Check out the Peano axioms.

[Anonymous No.7062089]

>inb4 Bourbaki

[Anonymous No.7062174]

>>7060544
moar

[Anonymous No.7062232]

>>7060491
fuck off.
>>7060463
OP, I've gone down this path only little ways so far, and it is astounding what you learn when you apply yourself.

what you really learn is how idiotic people are, they inundate the language of mathematics without even the slightest intuition as to how to creatively deduce anything true from it, aside from whatever another mathematician has conceived already.

the sort of arrogant stagnation of our education system the world over has to deal with these imbeciles, but you don't have to. Remember this formula

geometer + artist + mathematician + logician + philosopher + inventor = plato
mathematician = neuman
neuman = 1/6th plato
everybody here isn't a tenth as smart as neuman
neuman wasn't a tenth as smart as plato or Archimedes, yet their work is what lead to anything perceptive we deduce in math modernly.


in other words, everybody here is a complete fucking toolbag including myself, and I'm fine with that. I think admitting stupidity is the first step to learning fuck all.

[Anonymous No.7062237]

>>7060544
Is that Keira Knightly?

[Anonymous No.7062262]

If anyone knows integrals, please tell me can you learn integrals if I dont know all of the excerpts (limes, f(x) and shit like that).

xpoiguj23rfsf so its not a repost

[Anonymous No.7062271]

>>7062237
Obviously not.

[Anonymous No.7062285]

>>7062232
>neuman wasn't a tenth as smart as plato
lmao
why do you think that?

[Anonymous No.7062299]

>>7062232
>remember this formula about two people I never met
>formula about people
>that I never met, to boot
>u r all dumb, huehuehue

[Anonymous No.7062329]

>>7062285
have you actually read about this moron?
his political comprehension was that of an 8 year old smashing GI Joes together
he was a dim man with an aptitude, just like any other super-memory man, except he applied himself.

ever notice every single great mind drew? neuman didn't draw.

>Throughout his life von Neumann had a respect and admiration for business and government leaders

Neumann was a battery. He actively worked on many nuclear strategies and devices while believing and justifying their use.

Feynman questioned what he did and felt shame post Hiroshima. That's a smart man, not an unquestioning calculating tool.

Neuman was a sharp tool, but a Tool he was.

>>7062299
You can't translate the metaphor and pose an argument? The idea is that neuman was math, plato was far reaching.

I know this argument goes above your head because your translation of IQ is a linear point system with a powerful literate bias.

[Anonymous No.7062361]

>>7060544
>But to interpret the syntax you'll heave to study some first-order logic
This is hood advice. Learn logic first and then look for axiom texts like hilbert for geometry or peano for algebra

[Anonymous No.7062414]

Definition 1.
A point is that which has no part.
Definition 2.
A line is breadthless length.
Definition 3.
The ends of a line are points.
Definition 4.
A straight line is a line which lies evenly with the points on itself.
Definition 5.
A surface is that which has length and breadth only.

[Anonymous No.7062418]

Pick up a copy of Spivak's Calculus. Something I've learned during my education is that calculus is inherently geometric, making it actually pretty intuitive, despite the god-awful teachers of today ruining it. Spivaks book is really accessible and introduces a lot of fundamental aspects of mathematics that most courses don't bother touching.

You may want to also pick up a book about set theory. It's a very elementary and fundamental area of mathematics, upon which one could argue the rest is built. I have a book called Sets and Groups, which is really good. I cannot remember the author's name at the moment, but if you type that in in Amazon, it is the book with the black cover.

[Anonymous No.7062441]

>>7062329
>ever notice every single great mind drew?

WAT