WHY DO MATHEMATICIANS ACCEPT THIS NONSENSE? IT IS THE ROOT OF EVERYTHING WRONG WITH MATHEMATICS

WHY DO MATHEMATICIANS ACCEPT THIS NONSENSE? IT IS THE ROOT OF EVERYTHING WRONG WITH MATHEMATICS

>continuing a sequence indefinitely is nonsense
>but arbitrarily halting the progression of a sequence is also nonsense
hmmmmmm

What's wrong with it?

INFINITY DOESN'T EVEN EXIST. SHOW ME A SET OF INFINITE APPLES

Let {A} be the set of all apples that will grow under the following conditions:
1. Apples never go extinct
2. Apple farmers never go extinct

Infinite apples don't exist, so the set of infinite apples is the empty set which can be presented as a set of zero apples.

THE AXIOM OF INFINITY DOESN'T SAY SHIT ABOUT SEQUENCES. IT STATES THAT THERE IS A SET WITH INFINITE ELEMENTS WHICH DOESN'T EXIST IN THE REAL WORLD ONLY IN MATHEMATICIANS IMAGINATION.

>1. Apples never go extinct
>2. Apple farmers never go extinct

NOT REAL WORLD, THAT'S FANTASY. AND ANYWAY WITH THAT CONDITIONS, AT ANY GIVEN TIME THERE WOULD BE SOME FINITE NUMBER OF APPLES IN THE SET, NOT INFINITY

>the set of infinite apples is the empty set

I BET YOU ARE ONE OF THE GUYS WHO ALSO CLAIMS THAT THE SUM OF ALL NATURAL NUMBERS IS NOT ONLY A NEGATIVE NUMBER BUT ALSO A FUCKING FRACTION

There are no perfect isosceles triangles in the real world, either. I guess we should throw away trigonometry and just bang rocks together and make grunting noises for the rest of eternity.

Hello OP, I am a representative from the Vatican. Unfortunately, your thread is heretical and against His Holy Church. Infinity is not to be questioned, such is His will.
Your location has been logged. Please cease the creation of all threads and posts regarding infinity or we will dispatch a field team to remove you.

Go away Norman

SEE THIS IS WHAT HAPPENS WHEN YOU TRY TO EXPOSE MATHEMATICIANS LIES, THEIR FRIENDS TRY TO SILENCE YOU

Lets take a round object.

We measure its diameter to be r

we then begin measuring around the circumference, marking off distances 3. We cut out the sector between 3 and 0. Did we cut into some extra demension, or is there a cut at a fixed point?

pi is rational.
QED

Neither do imaginary apples, nor negative apples. Shall we toss those as well?

YES

Axiom of infinity is not the root of set theory's problems; the real culprit is the axiom of foundation.

Instead of outright banning all infinite descending membership chains they should have assumed instead that every non-empty set contains at least one finite descending chain.

What's the area of an apple?

It doesn't exist in THIS world

You think I'm joking but I'm not

The unmemed memer is infinity

> Implying apples exist.

>It doesn't exist in THIS world

THIS IS THE TYPE OF ARGUMENTS MATHEMATICIANS USE TO JUSTIFY THEIR NONSENSE.

>MUH OTHER WORLDS
>MUH TIME TRAVEL
>MUH APPLES THAT NEVER GO EXTINCT

Point two mirrors at each other. What is the resulting image if not real world infinity? Yes it's not perfect like no real world sphere is perfect, but the underlying 'mechanism' that is responsible for this effect is very much real.

BULLSHIT THERE ARE NO 100% REFLECTIVE MIRRORS AND SO THE LIGHT CAN'T KEEP BOUNCING INFINITELY BETWEEN THEM

NEXT

This is next.
Come at me bro.

Asking the real questions here.

This only proves pi is real, not rational. Only way to express this is (pi-3)/pi, not as a proper fraction

>I BET
there is no wagering at Veeky Forums, Grandpa pls

You didn't even try to understand. Never mind

>AT ANY GIVEN TIME THERE WOULD BE SOME FINITE NUMBER OF APPLES IN THE SET, NOT INFINITY

what is the most amount of apples there will ever be?

The universe is infinite. The event horizon of a black hole is a perfect circle. Get bent loser.

you're idiots

Seriosu they're just an emergent phenomenon of interactions between fields

All maths aren't real.

time travel?
other worlds?
he is talking about plato's world of forms, the world of abstract objects you brainlet

>WHY DO MATHEMATICIANS ACCEPT THIS NONSENSE?
Because it creates very nice theories and fits the way we view the world very well.
We dont see space as something disjointed and made up of finite parts even if it is completely discrete.

Unless finitists provide alternatives to stuff like DEs and Integrals which lead to equally nice results and are as applicable to model reality it will stay irrelevant.

Numbers don't even exist, my dude. Neither do sets, functions, or even logic. They're just things we make up.

take your meds and get some rest Grandpa, pls

They accept it because it's useful. Real Numbers makes calc really easy, and calc is really useful.

Sure, there probably isn't an infinite amount of anything in the universe, unless the universe in infinite, but surely you'd want items is the universe to belong to the same set? And you simply can't have an upper bound on that set, so in effect there infinite sets that objects belong to.

>implying math has anything to do with the real world
lol

infinity exists, apples don't

The set of all apples that are, have been, and possibly may be.

The only thing you can say truly exists is what you can see right in front of you. And even that can't be 100% proven that its real. How can you be so sure you're not currently trapped in an insane asylum just imagining being free from the confides of your padded room?

>How can you be so sure you're not currently trapped in an insane asylum just imagining being free from the confides of your padded room?
I can because only rationalists discriminate between imagination and ''reality'' and because claiming that something is imagined is already claiming that that it is not real and that there is a procedure to see how unreal it is

The set of all seconds from the beginning of the universe to it's end.

The appearance of material objects has no correlation with the collective conscious knowledge of any and all numerological reductions of said objects.

>tfw this kind of discussion is as close as most stemlords will ever get to looking behind the veil

It gives us interesting mathematics. Honestly, what better way is there for picking axioms?

UNDEFINED. BECAUSE IT IS AN IMPOSSIBLE SITUATION THATQUESTION MAKES NO SENSE

>The universe is infinite.
NOT PROVEN. ALSO IF WE LIVED IN SOME GIANT PLANET IT WOULD LOOK LIKE IT NEVER ENDS BUT THAT DOESN'T MEAN IS INFINITE

>he is talking about plato's world of forms, the world of abstract objects
NOT REAL WORLD

BUT NATURAL NUMBERS REPRESENT ACTUAL THINGS OF THE REAL WORLD, SO THEY'RE ACTUAL NUMBERS, THE REST IS IMAGINARY CRAP

VERY LARGE NUMBER != INFINITY

Good to see you again, CAPfag. Still fighting the good fight I see.

SERIOUS MATHEMATICIANS SHOULD START A NEW SYSTEM WITHOUT THE INFINITY AXIOM, THERE IS A REASON WHY MOST PEOPLE HAVE A HARD TIME GETTING THE CONCEPT OF INFINITY IN MATHEMATICS. BECAUSE IT IS MADE UP CRAP

Do you agree with the concepts of 1, 2, 3, 28148218, etc? Do you agree that if x is a number then we have an algorithm to generate a representation for x+1 and know that it is a number as well? Do you agree that it thus makes sense to talk about the set of all such numbers? This is the axiom of infinity. You could literally replace it by "the natural numbers are a set" and you get the same theory.

>Do you agree with the concepts of 1, 2, 3, 28148218, etc?

YES, BUT ACTUAL NUMBERS REPRESENT REAL WORLD THINGS

>Do you agree that if x is a number then we have an algorithm to generate a representation for x+1 and know that it is a number as well?

YES BUT AT SOME POINT X+1 STOPS BEING AN ACTUAL NUMBER AND BECOMES IMAGINARY CRAP SINCE IT DOESN'T REPRESENT ANYTHING IN THE REAL WORLD.THERE IS NO REAL WORLD INFINITY

You can let it fall, no problem. But then you drop out of the level of which ZFC is part of in the godel hierarchy (you end up in the same level as basic number theory, if I'm not wrong. So, a really weak system).

Math is an abstract world, as other anons already tried to explain to you, nothing (math concepts) exists in "reality" (although, concerning infinity, one can argue: If I can think of infinity, and my thoughts are "real", then infinity exists in reality). Natural numbers don't exist in reality: Assume there is no infinity in the real world. Then the set of all things in the universe is of finite cardinality N, but what is N+1 then? Does not exist in reality but is a natural number.

>YES
no you don't agree you imbecile. you don't agree that if X is a number then X+1 is a number. that's literally the axiom of inifinity

Wildburger pls go

Math isn't concerned with what is real. Only with logical structures.

Natural numbers don't represent actual things. There're just symbols used in the placeholder of counting. You can show me 3 of something but you can't show me 3 itself.

>implying time flow will ever end

TOO LARGE NUMBERS DON'T EXIST

>there exists some arbitrary point such that x+1 isn't a number
But y tho

BECAUSE AT SOME POINT THE ``NUMBERS'' BECOME IMAGINARY CRAP, IT'S LIKE SAYING SOMEONE HAS -5 BROTHERS

>at some point
Which point? And that's a really shit analogy

where do you find numbers in the real world ?

obviously you can't say at which point, because the point doesn't exist

I wonder what the consequences of such an axiom would be

Math would obviously be totally broken. You have to drop the union-axiom, power-set-axiom, pairing-axiom etc.,.... And there is nothing interesting going on there.

>>Veeky Forums
Stay in your containment board, Rei

Do you believe in the existence of pairs? I. E. Can I take two things, say two stones, and consider them together as one, as a pair of stones.

Lewis Carrol pls leave

I'm positive i've seem this exact same thread before.

are we in the Berenstein universe?

Memes aside, I started only recently to have an axiomatic study of set theory.
When I got to the infinity axiom I was.... disapointed. I have no problems with the concept of infinity, but I was hoping to be proved in a more elegant way than just taking an axiom like this, perhaps based on some more simple intuitive axioms.

> I was hoping to be proved in a more elegant way than just taking an axiom like this

If you drop it, you can't proof it from ZFC: (ZFC-INF) =/=> (ZFC).
If your axioms only allow sets with finite cardinality, you can never get to a set with infinite cardinality.

How can apples be real if particles aren't real

Serious question

Show me a set of -1 apples. Validity of mathematical concepts is not determined by whether they can be represented with apples

Funny, but actually the church was against the concept of infinity, because as they said, if we fill the universe with our infinity then there would be no space left for God.

Look up spinozas opinion on infinity,
He puts it nicely

Then there could be a set A such that A={1,A}, and that seems a bit counter-productive.
It doesn't make more sense then A={A}.

...

If God was so great he could have created enough space in the universe for both.

Look up semiring theory. You just have a number for "everything beyond the arbitrary cutoff".

No there is a bigger problem with one set of infinities being bigger than another. It seems like it makes sense and doesn't at the same time.

OP has a point, there is no empirical example of anything infinite. I debated this online with someone ten years ago and they just kept begging the question over and over again like a little bitch.

how about the amount of stupidity of anons on this shit website?

Either the number of times you can add a natural number to 0 such that the result is still a natural number, or (if that's not empirical enough for you) the number of points between any two distinct objeccts.

If they object to the latter based on Planck length or quantum theory, then point out that the theory of quantum physics presupposes the natural numbers (you can't do quantum physics in ZFC-Axiom of Infinity) so if they believe in the validity of quantum physics then they must a priori believe in the existence of the natural numbers, so you can then take that as an example of infinity.

>Either the number of times you can add a natural number to 0 such that the result is still a natural number
This one is pretty silly, the number obviously doesn't exist. It can't be infinity, because by then you've reached infinity and infinity isn't a natural number thus contradicting the claim that it is still a natural number.
>the number of points between any two distinct objeccts.
And for this, the obvious response would be that mathematical points of no measure or size don't even begin to exist to begin with.

not an argument bitch.

AND THIS IS THE PROBLEM WITH MATHEMATICS, STUFF LIKE ``DIFFERENT SIZES OF INFINITY'' IS ACCEPTED WITHOUT QUESTION, EVEN THOUGH WHEN FIRST INTRODUCED TO MOST PEOPLE IT JUST MAKES 0 SENSE BECAUSE IT'S BULLSHIT

THE ONLY LEGIT ANSWERS DEFENDING THE AXIOM OF INFINITY IN THIS THREAD WERE

>BECAUSE IT PRODUCES SOME COOL RESULTS

OKAY NO ONE IS AGAINST THAT, BUT AN AXIOM SHOULD BE SOMETHING THAT'S CLEARLY TRUE AND THE AXIOM OF INFINITY ISN'T, MATHEMATICIANS USE IT WITHOUT AN ACTUAL REASON

OF COURSE YOU CAN'T PROVE SOMETHING THAT'S CRAP!

>IT STATES THAT THERE IS A SET WITH INFINITE ELEMENTS WHICH DOESN'T EXIST IN THE REAL WORLD
Spacetime is continuous and hence has infinite points.

NICE CIRCULAR REASONING

>ctrl+f: 'real world'

>14 results

Holy... you really think it exists? I can't find it anywhere. All I find is more qualia, nothin' but qualia around. Oh, there's another one!

Infinity is proved you little bitch.

>he's this much of an engineering pleb that he thinks we need an empirical referent for the truth of mathematics
>dude what is set theory lmao

> axiom of infinity
> axiom
> proved

I am requesting an empirical example of something infinite which means it needs to be physically observable or based on experience, I am not requesting a proof of infinity is based on theory or logic.

LOL

Why do people accept god?
It makes things easy just like infinity for mathematicians.