/sci/ - Science & Math

[Anonymous No.10982515]

Obviously numbers exist.
Real question is what else does?

[Anonymous No.10982522]

>>10982515
Daily reminder that contemporary mathematics is based on axiomatic believe system.

[Anonymous No.10982527]

why deny the reals, their practicality alone justifies them

[Anonymous No.10982544]

for me, it is countabilism

[Anonymous No.10982557]

>>10982522
What is the difference between definition and axiom?

[Anonymous No.10982560]

>>10982515
>Obviously numbers exist
Many philosophers disagree. Google sep number theory

[Solivagus No.10982562]

>>10982557
Period length of utilization. The four operations of mathematics: +-/*

They all operate on the comparative: =

[Solivagus No.10982565]

>>10982557
Dictionary definitions update more frequently than mathematical functions/equations.

[Anonymous No.10982590]

>>10982557
Axiomatic believe system is equivalent to religious dogmas.
You dont question them just take it for granted.
This is where math departs from science.

[Anonymous No.10982604]

what race is he? why is he so dark?

[Anonymous No.10982613]

>>10982604
Australia mate,sun is hot there.

[Anonymous No.10983147]

>>10982527
> the reals, their practicality
What did you mean by this.

It's rare that any engineer even uses formal field extensions - only some physicists do when the work with mathematica. Most of the time they work with 16-digit approximations of real numbers. Would be interested we we lived in a world where you could even calculate with the reals. Try doing Newton method without truncating at each and ever step. You can't even use the method using Q, let alone R.
The reals are "used" in algorithm descriptions to not having to track error terms of trigonometric functions and roots - that's about it.

>>10982557
Axioms make a hoc judgement about boolean sentences. Definitions introduce symbols and their subsitution rules.

If you work within an axiomatic framework, often people introduce predicates that aim at specifying / pinning down a certain set of object (e.g. you formally thin of yourself workin in a set theoretic grounding and talk about groups - then you say what a group is and continue working with sets that, explicitly stated or not, are restricted to those fulfilling the group axioms). In that case, it looks like an axiom, but in reality you're just introducing a conditional for all statements that follow.

[Anonymous No.10983152]

>>10982527
> the reals, their practicality
What did you mean by this.

It's rare that any engineer even uses formal field extensions - only some physicists do when the work with mathematica. Most of the time they work with 16-digit approximations of rational numbers. Would be interested we we lived in a world where you could even calculate with the rational. Try doing Newton method without truncating at each and ever step. You can't even use the method using Q, let alone R.
The reals are "used" in algorithm descriptions to not having to track error terms of trigonometric functions and roots - that's about it.

>>10982557
Axioms make a hoc judgement about boolean sentences. Definitions introduce symbols and their subsitution rules.

If you work within an axiomatic framework, often people introduce predicates that aim at specifying / pinning down a certain set of object (e.g. you formally thin of yourself workin in a set theoretic grounding and talk about groups - then you say what a group is and continue working with sets that, explicitly stated or not, are restricted to those fulfilling the group axioms). In that case, it looks like an axiom, but in reality you're just introducing a conditional for all statements that follow.

[Barty Crouch, Jr. No.10983857]

I think, therefore I am.

[Anonymous No.10983928]

>>10982544
Source?

It's pretty unnecessary they introduce the symbol N and then use mostly w anyway.

[Anonymous No.10984009]

>>10983152
There's a few proposed methods to do "exact" calculations with reals, replacing irrational numbers with functions that compute them up to a desired precision only when evaluation time comes (it's a bit different from the stuff you mentioned from Mathematica), but it's so slow it's unlikely to become widespread.

[Anonymous No.10984026]

>>10984009
Reference?

[Anonymous No.10984031]

>>10982590
>Axiomatic believe system is equivalent to religious dogmas
???

[Anonymous No.10984056]

>>10984026
Someome posted a few papers about it on /g/ forever ago. It was from a dude with a finnish/scandinavian/whatever name, sorry.

[Anonymous No.10984063]

>>10982590
So what's the alternative?
>>10982522
So?

[Anonymous No.10984080]

>>10982515
Numbers are the measure of something, if there weren't things to count in the real world, numbers wouldn't be a thing.

[Anonymous No.10984083]

>>10982590
>there are no axioms in science

[Anonymous No.10984450]

>>10984080
You dumb motherfucker. Someday you must answer to a god who will not be as forgiving as us

[Anonymous No.10984478]

>>10982590
>calling math something that isn't a axiomatic believe system

[Anonymous No.10985244]

>>10982590
this but unironically

[Anonymous No.10985253]

>another IQ thread

[Anonymous No.10985495]

>>10982515
We know numbers exist so knowledge must exist too, along with everything relevant like minds and thought.

[Anonymous No.10985694]

>begin with zero
>construct a successor function
>construct a number s.t. [math] n + n_0 = 0 [/math] [math] \forall n\in \mathbb{N} [/math]
>construct the rationals by using ordered pairs [math] (p,q) [/math] with p,q from the previous set s.t. *insert properties of the rationals in terms of ordered pairs*
>notice that there exist some numbers s.t. no p/q represents them
>define them as the completion of the rationals
what is the controversy?

[Anonymous No.10985700]

>>10982590
>TFW my pastor was right, every path takes you to god.

[Anonymous No.10985797]

>>10985694
That you can only define "them" as a collection, not on an individual level, and not in a finite way (as you can do with rationals).
The reals are both not needed while at the same time introducing in-elegancies. That's not to say you shouldn't study them. They are an interesting formal conception.

[Anonymous No.10986008]

>>10985797
>The reals are both not needed
wut? how would you express the length of the hypotenuse of the right triangle with sides 1 and 1?

[Anonymous No.10986018]

>>10986008
Working with countable transcendental extensions over the algebraic numbers
https://en.wikipedia.org/wiki/Algebraic_number

Any alphabet one may ever use and each specification is finite. Most reals can't even be conceptualized as individual numbers in principle, let alone defined.
https://en.wikipedia.org/wiki/Definable_numbers

[Anonymous No.10986079]

>>10986018
Alright, then what do you call the ratio of the diameter of a circle and its circumference?

[Anonymous No.10986083]

>>10982515
The Universe.

https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis

[Anonymous No.10986086]

>>10982515
What does Wildberger think the square root of 2 is?

[Anonymous No.10986087]

>>10986086
His issue is actually with transcendental numbers, not irrational numbers.

[Anonymous No.10986088]

>>10986079
That's just pi bro.
One way to get approximation is by truncating the continued fraction
[math] \pi= {3 + \cfrac{1^2}{6 + \cfrac{3^2}{6 + \cfrac{5^2}{6 + \cfrac{7^2}{6 + \ddots\,}}}}} [/math]
You can adjoin those in extensions to your algebra and I'm ready to answer a countable amount of your questions if you really want. But I won't adjoin non-computable numbers.
https://en.wikipedia.org/wiki/Computable_number

[Anonymous No.10986090]

>>10986088
But I won't adjoin non-computable numbers - nor an uncountable amount of those.

[Anonymous No.10986092]

>>10986087
Okay, then what does he think the ratio of the circumference of a circle to its diameter is?

[Anonymous No.10986093]

>>10986092
see >>10986088
Basically, if a number can be shown to have any relation to reality, it's good

[Anonymous No.10986098]

>>10986093
How does he tackle nonreal zeros?

[Anonymous No.10986103]

>>10986088
I did some research into this. Apparently the vast majority of real numbers aren't definable? What the fuck?
https://en.wikipedia.org/wiki/Definable_real_number

[Anonymous No.10986105]

>>10986092
He defines it in his book on page 267 as
[math] \pi = \int_0^1 \dfrac {1 } { \sqrt{s(1-s)} } ds [/math]
and gives the procedure in pic related to compute

http://www.ms.lt/derlius/WildbergerDivineProportions.pdf

[Anonymous No.10986117]

>>10986103
This is obvious, since the descriptions of a fixed alphabet can be enumerated. Say the alpabet we want to use has 256 character
>abc...xyzABC...XYZ+'#-.;....0123456789

and enumerate all books by

>a,b,c,...,7,8,9,aa,ab,ac,...a9,ba,bb,bc,...aaa,aab,...
etc

If you use sets which constructivel can't be enumerated (put in correspondence with the first countably infinite ordinal, say N), then you can't describe (or conceptualize in your head) all its elements as individuals.
Set theory is able to characterize collections as a set, but not seperate out all their contituents.

[Solivagus No.10987837]

>>10986105

[Anonymous No.10988328]

>>10986103
>>10986117
So the vast majority of real numbers don't really "exist" in a meaningful sense because they don't real

[Anonymous No.10988339]

>>10988328
rip
the math mafia got him