Is the mathematical concept of infinity real?

Otherwise Zeno's arrow paradox cannot be solved. To reinstate quickly what the "paradox" is:

- An object traveling from A to B has to pass point C, which is 1/2way between A to B. This is of course experimentally observable
- An object traveling from C to B has to pass point D, which is 3/4 way between A to B and halfway between C to D. This is of course experimentally observable
- An object traveling from D to B has to pass point E, which is 7/8th way between A to B and halfway between D to B. This is of course experimentally observable

So on and so on.

The paradox is not solvable without the concept of limits where 1/infinity = 0. This is also the foundation in which Newtonian calculus is built on. Seems like a irrefutable empirical evidence for the concept of mathematical infinity

Nope. Godel's Incompleteness Theorem implies that the axiom of infinity is inconsistent.

How would one solve Zeno's arrow paradox then? Without the concept of limits, the arrow would never reach B as it goes infinitely close to B in [(2^n)-1]/(2^n)

>without the concept of limits where 1/infinity = 0

dafuq user? do know how a limit works?

Most of math isnt "real"

But 0,99999...... = 1

great question. infintesimal infinity only exists mathematically. universe space-time has smallest component known as planck area.

>planck area
This is a limit on human investigation not a limit on reality

the reality is we traverse by quanta in three dimensional space. get over it.

Idiot

Probably sure. What does that have to do with anything?

how is this a paradox? if the arrow reaches the target, it obviously passed point C no matter where it was

It's a philosophical paradox

- An object traveling from A to B has to pass point C, which is 1/2way between A to B. This is of course experimentally observable
- An object traveling from C to B has to pass point D, which is 3/4 way between A to B and halfway between C to D. This is of course experimentally observable
- An object traveling from D to B has to pass point E, which is 7/8th way between A to B and halfway between D to B. This is of course experimentally observable

So on and so on, in which the foundation of said logic is irrefutable. If so how come A ever reaches B? Based on this line of reasoning the arrow would've never reach B as it goes infinitismally close to it.

This is why science > philosophy

Things do cross distances, so clearly the assumptions of the paradox are wrong. Case closed

i see, thanks for explaining it to me

>universe space-time has smallest component known as planck area.
No, Planck length is not the minimal length possible, it's only the length where effects of quantum gravity start to be so relevant that cannot be ignored any longer.

Any modern philosophy that's worth a damn involves high degree of math though, as they learn from Zeno's arrow paradox philosophers were arguing and groveling in the mud for close to 2000 years before Newton came by and solve the problem mathematically. I think modern philosophers understand that.

However, one of the foundation of newtonian physics is differential calculus, which hinges on limit and to solve limit as n->infinity one needs to "accept" that 1/infinity is mathematically equals zero.

planck area is the smallest area to exist in physical space

Space is continuous and cannot possibly be discrete based on Einstein relativity where space and time is stretchable.

If space is fundamentally discrete, then under relativity as you stretch space it'll become jankier and jankier just like how you expand a jpeg file into a bunch of discrete pixels. As far as we know, this is experimentally proven to be untrue

this. the experiment of reality proves distances are closed. doesn't mean we cant use mathematics to approximate reality

einsteinmanstein wasn't right about everything. fact is we close distances that aren't philosophically or mathematically possible.

- An object traveling from A to B has to pass point C, which it does. This is of course experimentally observable
- An object traveling from C to B has to pass point D, which it does. This is of course experimentally observable
- An object traveling from D to B has to pass point E, which it does. This is of course experimentally observable

Any point between A and B, the object has to pass. Which is does. And is experimentally observable. Solved.

>planck area is the smallest area to exist in physical space
You cannot say that without a theory of quantum gravity.

the question is how, if it is passing an infinite amount of sections of distance as soon as it starts moving

yeah, I was pointing out the 'wordplay' that most of these paradoxes dwells on. We are just constructiong the notion of mathematical infinity and dividing the length from A to B infinitely. On the otherhand, given OPs assumption for infinity is true, then we can say the same not just for the points between A and B, but the position of the arrow head as well.

Because 1 unit of energy (smallest amount of energy commonly transferred between atoms) results in x amount of movement. no less, no more. It's not possible for it to move only 1/(some big number).

>position of the arrow head as well.
god dammit this makes sense. how can the arrow reach the 1/2 distance point. how can 1/2 the distance even be taken? point A and B are the only known quantities

no the jews invented it to prevent mathematicians from solving the Riemann hypothesis

ITT: retarded metaphysics meet retarded metamathematics

>before Newton came by and solve the problem mathematically
how did he "solve" the problem?

sigh, slap a greek name on something and the lib arts majors will never stop naval gazing over it

Yes space is continuous, yes the arrow passes infinite points, yes classical mechanics assumes space continuinity, no it doesn't prove the universe is infinity

how long until a particle physicist invents "dark infinity" to account for a discrepancy in the standard model?

>The paradox is not solvable without the concept of limits where 1/infinity = 0.
Lol, this is hardly a good paradox.
It's about the same level as "why do we park in the driveway, but drive on the parkway?"
Zeno never addresses what happens one second after his infinite regression point.
Instead, he avoids looking at he actual finish by delving deeper and deeper into irrelevant minutiae.

This so much.

just wanted say first off theres no convincing science that infinite cannon finite doesn't convince . you should just be wondering how many and how little words are to robots

Are you guys stating that the arrow will reach the target at the time [math]t\infty[/math] ?

no infinity is a meme of math a great idea that is not right.
there is an end to all things even math.
pick related if infinity was real this would have never stopped.

>Someone who doesn't understand the implications of Godel's Incompleteness Theorem

It would take an eternity to cross one meter divided into infitesimal steps

no because infinitesimal steps are crossed in infinitesimal time, i'm shit in maths but bro.. it's just logic

Take real analysis. Zeno's paradox is only true after finitely many iterations. Infinitely many, and it does touch the point. That's how limits work.

what you are really asking is if the universe is continuous or discrete

Discrete is the right answer. Besides Zeno's paradox isn't a physical analogy, anyone who claims it is is a retard. The arrow would only not touch if it slowed down inversely proportional to how far it moved, which describes literally nothing physical.

Zeno's paradox is and always will be about the existence of irrational numbers, e.g. pi and roots of some integer polynomials, problems the greeks were well aware of.

As to the OP question if infinity is "real", it's a stupid question because a lack of infinity is inconceivable. Infinity has to be something we "get" intuitively. What's more remarkable is the work of Cantor.

I don't think that's right. Pretty sure Zeno's paradox was about proving Parmenides right.

Infinite space in finite time doesn't make sense, therefore motion is an allusion. He had a bunch of other paradoxes that said similar things, i.e things being bigger or smaller is incoherent, multiple things being incoherent.

>,

The point is not to prove that things don't move, it's to make you question which of the assumptions are wrong, retard.

The greeks knew geometric sums converged. The "paradox" is they didnt believe in infinite divisions. The arguments by parmenides are more "paradoxes" to be solved than they are actual arguments about the state of affairs. Clearly objects move.

>The "paradox" is they didnt believe in infinite divisions.
Even if this was the contention it still doesn't make sense, because space does seem to be continuous/infinitely divisible and yet objects move no problemo.

Get this mate:

You have 1/a

The bigger a gets the smaller the whole expression becomes..

Some might say as a gets to infinity the expression becomes infinitely small... To the point where it becomes zero.

But no one takes those sad cunts seriously.

Nice semantics problem bro.

Physically there is no paradox, because we can observe that the arrow indeed reaches it's end.

Mathematically, the arrow only reaches it's end at a limit. Without the notion of limits, it is indeed never going to reach it.

Why do you think there is a problem with this?

Again its not about actual objects, its about convergence and limits.

>in real life we can observe an infinity time

>one needs to "accept" that 1/infinity is mathematically equals zero
no! you simply do not understand limits then.
all lim n-> infiniy 1/n = 0 means is that FOR ANY e > 0 (so even for super small ones) you can find a natural number n0 for which 1/n - 0 < e holds true for EVERY n > n0. there is no 1/infinity involved

i never thought this was possible but Veeky Forums really took raw numbers and made them into memes

it's not an infinite time, it's a finite that can be mathematically represented by infinite infinitesimals.

...

That's just wrong.

>Abstraction to fit reality, invent concept, draw conclusion from abstraction that concept exists in reality
???