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

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

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

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.

[citation needed]

highschoolers do not belong on Veeky Forums

Are you saying that no set of axioms is consistent?

brainlet

Look up euclidean geometry numbnuts

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

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

youtube.com/watch?v=SrU9YDoXE88

Not if the system isn't complete

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

There's always more

sure, if that's what you believe

>vsauce

pop-sci garbage for normies. No thanks.

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?

Have you built our warp drive yet oh mighty one?

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.

...

en.wikipedia.org/wiki/Banach–Tarski_paradox

> Doesn't know what a paradox is

youtube.com/watch?v=3bacYDSy19Q

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

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

>can't possibly falsify it
its shite

hah!

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?

They have different cardinality

Hey user, 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

Aren't most of those, like philosophical issues

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

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.

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

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.

Praise.

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?

bugs in the computer code

sizing up that lamb for a kebab

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

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

G-guys?

undefinability of truth
what do I win?

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

>t. empirishitter

>not knowing about ordinal arithmetic
stop posting any time

teach me, senpai

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?

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.

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

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

Euclidean geometry is fucking boring, bro.

divide by zero

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

> 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.