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/sci/ - Science & Math

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9168203 No.9168203 [Reply] [Original]

if math is sooo goood how come there exists paradoxes in it?

>> No.9169549

>>9168203
>there exists paradoxes
Get off brainlet, no human discovery or invention is perfect.

>> No.9169566

>>9168203
Because math is too good for us mere humans and for some reason there seems to be some entity that does not want us to be able to prove everything.

>> No.9169660

>>9168203
Something with paradoxes in it is more beautiful than one in which there aren't any.

>> No.9171405
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9171405

>>9168203
Hey physishit, did you know that your entire field, and all it's lower dependent fields (aka everything but math) are dependent on RANDUMB VARIABLES???!!!!!

AAHAAAHAAHAHAHAHAHHAHHHHAHAHAHAHHHHAHAHAHAHAH PHYSISHITS KEKED BY NATURE HAHAHAHAHAHAAA

>> No.9171441

>>9169549
>>9169566
or perhaps it's just an axiomatic issue...

>> No.9171455

There are no paradoxes in math

>> No.9171479

>>9171455
>there are more infinite reals than infinite integers

Bravo

>> No.9171649

>>9171479
how is that a paradox?

>> No.9172013

>>9168203
>if theories are so good, how come we can create a valid hypothesis to disprove them?
>also, how does the scientific method work?

>> No.9172026

>>9171455
It's mathematically proven that paradoxes will always exists no matter what base axioms you choose.

>> No.9172186

>>9171479
well there is an infinite number of reals between 2 integers so one infinity is bigger than the other

>> No.9172195

>>9172186
That's a poor reason. [math]\mathbb{Q}\cap [n,n+1][/math] has infinite cardinality, yet the rationals and the integers have the same cardinality.

>> No.9172344

>>9172026
[citation needed]

>> No.9172363

>>9172344
highschoolers do not belong on 4chan

>> No.9172745

>>9172026
Are you saying that no set of axioms is consistent?

brainlet

>> No.9172752

>>9172026
Look up euclidean geometry numbnuts

>> No.9172895

>>9172026
Define a theory with only one axiom [math]A[/math]. This theory contains no paradoxes.

>> No.9172906
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9172906

>>9168203
Oh wow hahah you're so cool bro you just learned what Godel's Incompleteness Theorems are woah bro you really did it man yeah man you really did it yeah dude show those mathfags what for man hahah niiice bro math is shit bro yeah man system of logic my ass man biology is way better man yeah bro hey bro do you want to hit the quad later and pick up some biology chicks man yeah bro these math nerds are really killing the vibe with their shitty and useless axioms bro let's outtie9000 this bitch

>> No.9173797

>>9172195
>>9172186
https://www.youtube.com/watch?v=SrU9YDoXE88

>> No.9173873

>>9172026
Not if the system isn't complete

>> No.9173932

>>9173797
I feel stupider after watching this video; was that the point of this video?

>> No.9173951

>>9173932
There's always more

>> No.9173965

>>9173951
sure, if that's what you believe

>> No.9173969

>>9173797

>vsauce

pop-sci garbage for normies. No thanks.

>> No.9173970

>>9173797
Vsause says:
>[math]\omega[/math] is just like any another number
In that case, what's [math]\omega / 5[/math]
Is [math]\omega[/math] a prime number?

>> No.9173975

>>9173969
Have you built our warp drive yet oh mighty one?

>> No.9173977

>>9168203
Like what? Using ZFC I don't think there are really any big issues. Sure some problems remain unsolved and some can't be solved. That doesn't mean there's anything wrong.

>> No.9173984

>>9173975

>>>/r9k/

>> No.9173986

>>9171455
https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox

>> No.9174216

>>9173986
> Doesn't know what a paradox is

>> No.9174620

>>9172186
https://www.youtube.com/watch?v=3bacYDSy19Q

>> No.9174960

>>9173986
Only an apparent paradox, to brainlets who don't understand it

>> No.9174971

>>9169549
>Logic isn't perfect
Name one (1) thing wrong with it

>> No.9174982

>>9174971
>can't possibly falsify it
its shite

>> No.9175187

>>9174960
hah!

>> No.9175298

>>9172186
But that just doesn't make sense. That isn't how it fucking works. Infinity is infinity. It is not quantifiable. One infinity cannot be "bigger" than another because they are still both infinite. How can you not comprehend this?

>> No.9175406

>>9175298
They have different cardinality

>> No.9175410

>>9175298
Hey anon, there are different types of infinities

countable vs. un-countable for instance

Countable infinities can be mapped to the integers (more specifically, the counting numbers 1+). Uncountable infinities cannot be mapped in that way because there are always extra in between that you can construct which do not match up (reals)

This is a really cool topic and once you underrstand it it really broadens your horizons, I suggest you take a class on introductory discrete mathematics and read up on set theory and propositional logic, then these topics will start making sense

>> No.9175413

>>9168203
Aren't most of those, like philosophical issues

>> No.9175420
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9175420

>>9174982
>can't possibly falsify it
That's why its so great you fucking retard

>> No.9175425

>>9174216
>>9174960
Not all paradoxes are formal logical contradictions. It's just such a weird result that it's really difficult to believe. The existance of non measurable sets itself is a paradox.

>> No.9175429

>>9175425
In that case OP is asking "If math is sooo good how come it's not 100% intuitive?" which is just dumb.

>> No.9175431
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9175431

One can never have moral objectivity. Plato tried to solve ethics but even he couldn't do it. Thay's why religion is the awnser.

>> No.9175713

>>9175431
>>9175431
Praise.

>> No.9175751
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9175751

>>9175431
Why do christposters always have the absolute worst taste in paintings? Is this an illustration from a kid's book? Do you like how this looks?

>> No.9175756

bugs in the computer code

>> No.9176108

>>9175431
sizing up that lamb for a kebab

>> No.9176139

>>9175751
What does it mean when the left tit is hanging out?

>> No.9176147

>>9175431
>religion is the awnser
More like, fawnser, am I right??


G-guys?

>> No.9177257

>>9174971
undefinability of truth
what do I win?

>> No.9177264

>>9172906
>Gödel's theorems
>saying anything about paradoxes
the only paradox here is how you're still alive

>> No.9177267

>>9174982
>t. empirishitter

>> No.9177270

>>9173970
>not knowing about ordinal arithmetic
stop posting any time

>> No.9177896
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9177896

>>9177270
teach me, senpai

>> No.9177916

>>9177270
Is ω a prime, or not? What's the value of ω/5?
What's ordinal arithmetic got to with those questions? Is this even addition/subtraction/multiplication/division in the classical sense, or are you creating more axioms?
>stop posting any time
Why are you so defensive?

>> No.9178229

>>9168203
There are certain axioms that were improperly defined in the past due to lack of information or foresight, yet are kept intact due to precedence, even though they create paradoxes and contradictions.

Math is like law in this regard.

>> No.9178772

>>9178229
CSfag here. This is why I'm learning math from Wildberger. Fuck every Mathematician who goes along with this shit.

>> No.9178830

>>9171405
>randumb variables
No true physicists believes quantum effects are truly random.

>> No.9178834

>>9172752
Euclidean geometry is fucking boring, bro.

>> No.9180499

>>9174971
divide by zero

>> No.9180506

the shapes you use to define counting things are outdated and primative. the notion of two identical anything doesnt exist and thats where arabic numerals begin to fail. Add on to this absolutely crackpot science being graded and forced down childrens throats, and you have our current system, its as primitave as cavemen art. alot of times its close and with enough fucknuggery even closer. but numbers themselves are not accurate at all

>> No.9180507

>>9168203
> if math is sooo goood how come there exists paradoxes in it?
Because it's good. Seriously.

Goedel's theorem relies upon predicate logic being capable of expressing its own metatheory. You can't pull the same trick with e.g. propositional logic simply because it's too limited.

The real take-away from Goedel's theorem is that /any/ formal system capable of expressing its own metatheory must be either unsound or incomplete.