Does infinity exist?

My ego lured me back. The weekend seems legit.

first I thought Serendipper had hit it on the head and nailed it but then I was convinced again by the argument about it being computable.

I thought it was pretty much standard approach though, that he started out with a definition that he just wanted to test.

The definition is pretty damn resilient in its ability to be validated, and also to clarify what we are talking about when we mean mathematical infinity.
As a way of nuancing you could suggest that infinity is a mathematical presupposition required to biject sets with their own subsets. Lol. I mean math is a circle, right?

As we know not in all logics the lack of yes means no and the lack of no means yes, some have for example null when the machine can’t allocate the question to an answer.

like if we apply Peano to a trivalue logic, for the proposition that the set of natural numbers is finite, we get not false but null.

Thats probably not irrelevant if you want to do quantum computing, which maybe for that reason hasn’t emerged yet even though they said they were about to crack it 20 years ago.

I think maybe you sometimes need to roll up infinities or wrap them up. I know thats what they do with whole dimensions in string theory.

Come think, every infinity is a dimension.
So thats why its a problem I see now that things can be present in different sets.

Yeah all this points to type theory, because it doesn’t predicate infinity but just allows for it, or basically allows for finitude to be endlessly postponed but still dominate whats actually there.

I think these are actually philosophical problems, like nitpicking, or being impossible, its really just showing the weak links in the theory, the points where it can be challenged. Its not an attack to destroy but to mine the rock for its minerals.

Also its a loss of pleasure. Infinity if it can’t be defined with some empirical tasty arguments, then the whole concept of it kind of diminishes. If you could show infinity to be as elegant as a galactic cylinder or matrix of primes - but well there you have it. Infinity is really well disclosed when you look at the logic behind the succession of primes.
There is absolutely no logic to be found. Thats a fucking infinity for the mind, a total mind bender, which is what infinity requires to be if it can be at all computed philosophically.
Because the phenomena that math describes are important, and it is not cool to have math deviate too lightly from these. Not out of conservatism, but a miners instinct… more knowledge might be scattered in the rocks nearby than far off.

Then how do you define infinity?

Unlimited in some ways and limited in others is unlimited in quantity and limited in identity/category. One thing is sure: we cannot have a quantity which is both limited and unlimited, so if there are limits, they are not imposed on the quantity that is said to be infinite, but rather they are imposed on the identity of the uncountable things.

I can’t conceptualize it and you can’t either. In actuality, where in the universe do you suspect that it may be possible to draw an infinite line in one direction, but not in the other?

Then, at this moment, it is not infinite because there exists a place for more road. How can you propose having an infinite road when clearly we could make it longer? A road that is truly infinite would extend around and around the universe many many times until it occupied every planck cube in the universe, completely displacing all matter, and until it eventually connected with itself for lack of having anywhere else to go. To say that isn’t so is to say the road has a boundary which would make it not infinite.

Ok, now I forgot why I needed to know that lol

Yes it does matter because if there is a place for another apple, but no apple is there, then we have found a boundary and therefore the number of apples is not infinite.

Size must have a zero like temperature and speed or else it couldn’t exist. We can’t get infinitely colder, infinitely slower, infinitely smaller and if we could, then temperature, speed, size would have no significance/meaning.

I think so.

I don’t know… maybe.

Infinitely wide is ok because it extends in both directions, but infinitely tall would be a wall that extends around the universe until it connected with the other side of the earth.

Huh? Infinite doesn’t mean maximized or maximal.

Pretend you’re talking to a 5-year old kid who doesn’t know what infinity means. If you say “we have an axiom of infinity”, the kid will look at you stupid. If you say, “we can align the set with a subset of itself”, the kid will look at you stupid. If you say, “the infinite is the unbounded, unlimited, unending” then the kid will say “Ooooh!” You cannot do any of these acrobatics (axioms, bijections) until you make it clear what infinity means.

There is no way I could perform a bijection of a set with a subset without already understanding the set is unending. So I would need to know what infinity means before I could understand the definition.

I accept that planets revolve around the sun not because of authority, but because it’s the most sensible scenario.

The infinite is something that cannot be observed (much like god) and there is no evidence for (much like god), yet I am required to prove that it doesn’t exist? There is also no evidence of a teapot orbiting the earth, so do I have to prove that doesn’t exist too?

What’s the biggest number you can think of? Now make it bigger: square it, factorial, define new symbols to reduce the size and continue on and on until you run out of room on the forum to write that number down. Regardless what you devise, you will find a biggest number, but you won’t be able to do anything with it other than bask in its glory.

The issue isn’t whether the bijection is possible, but whether it defines infinity.

I can integrate an area over a height to yield a volume without using infinity. I can add my grocery bill without infinity. What do you need infinity for?

What’s the limit of 1/x where x → 23+10^10^10^10^10^10^10^10^10^10? Zero right? If it’s not zero, then how far am I off? No machine that could ever exist will be capable of discerning the difference, so from the perspective of practicality, we don’t need infinity.

Induction isn’t the same as deduction and if n exists, you cannot say with certainty that n+1 exists. However, if n+1 exists, you can say with certainty that n exists (deduction).

Yes I understand your point, but we still must have a priori understanding that the turing machine never ends. Once again, infinity must be understood before it can be defined with the turing machine.

Yes it does because there are no boundaries. If there are boundaries, then it’s not infinite.

If you claim there are infinite apples and I find a place with no apples, then you don’t have sufficient apples to go around in order to fill every place and therefore the quantity of apples is limited or else there would be apples in every place that apples could exist.

If there could be an apple here, but there is no apple here, then the only reason to explain that is insufficient apples.

If I would claim there are infinite apples available, then yes that would apply. Also with one apple. But to have infinite apples in an infinite universe would not necessarily guarantee any apples within reach.

Like if time is infinite, which it is since beginnings are part of the concept time, then even if you are born now, some of your actions will still have effects for an infinite duration, unless the universe collapses into a singularity which I think is fantasy.

So your deeds would (do) resound in the infinite future, but not in the also infinite past.

Of course it would be easy to negate infinity if you start out with the assumption of a finite universe.

You can just say “the universe is finite, thus it isn’t infinite, thus nothing in it is infinite”.
But who will think this makes sense? Only people who already agreed with you on faith.

You can’t prove an end to the universe, or to a straight line, so to insist it does have one (i.e isn’t infinite) is like being really ambitious without any means.

So basically, an infinitely large basket isn’t going to be filled even with an infinite amount of apples. Because there still is space for an infinite amount of pears.

The whole thing is boringly easily solved when you see that infinite is a predicate and not a proposition.

So “infinity” of itself just means either everything or nothing. But any meaningful statement with infinity in it still gives infinity as a limited part of the proposition, where quality x or y or z is required to make the proposition.

“Does infinity exist” must mean “is existence infinite?”

And if it is, then all things must somehow reach into infinity too. And they do, by their consequences in time.

AH

fuck I understand.

the whole idea of a variable implies infinity.

So the Arabs who came up with algebra (with the contributions of a guy called Al Jabr) and also with 0 destroyed the Euclidean and Parmenidean idea of numbers as elements of a world, and made them magical appearances defying apparent reality yet working very well with the brain.

But this defiance can be because whats defied is what wasn’t proven yet. Maybe they were like hold on, its taken pretty long now that we sought for the end-all, and we didn’t find it so lets just suppose it goes on forever. Then at least we can be free of this supposed end-all and appreciate what we really see.

In my understanding, both 0 and infinite are predicates, and for X=existence they give respectively false and true because otherwise the concepts are contradicted.

If the axiom is “something exists” then for 0 to be true there needs to be a thing that is withdrawn from another.
For infinity to be true there needs only be one thing, it just needs to be infinite. So 0 is a higher order operator than infinity.

Still, infinity is a higher order principle to 1.

2 and uncountability are the same by implication because to get from 1 to 2 you need an assumption, which is that things are separate and not unified, and if you do that there is certainly no way of demonstrating any limits to the number of things that can be listed. And infinity is a higher order function of uncountability.

Only after all this is fixed we get to 0.
Or while its not being fixed but then 0 is seen as the basic depth of the thing where it is actually the summit.

Infinity is the root of all hypothetical numbers, including 0. 1 is the only non hypothetical number because it is the only number which can contain all others.

???. Doesn’t parse at my end.

Infinity can’t be true or false. It’s not a thing that can be true or false. A set being infinite might be true or false. Precision is critical.

Doesn’t make sense to me.

Order of what? Haven’t seen order defined.

Nonsense.

More nonsense. I have one apple, I have two apples. I have no idea what you are talking about. Have you a reference so I can have some clue as to what domain of discourse you’re working in?

Doesn’t parse. Says nothing. Word salad.

After all what is fixed? What’s broken?

You often make sense. This post of yours does not make any sense.

What is a hypothetical number? What other kinds of numbers do you have in mind that aren’t hypothetical? The root? Like the root of a polynomial, or a square or cube root? You’re just throwing out random words. This is unlike your usual posts, which are generally connected with reality and sense.

Bullpucky.

Isn’t the collection of even numbers infinite? They’re clearly only a part of something larger. They’re not everything. They don’t include the odd numbers, for example.

I see you wrote several posts, not just one. But you seem to have decided to wake up this morning and post strings of word salad, devoid of meaning or sense. I don’t mean for that to be an attack. Only an observation. I’ve come to expect sensible posts from you. If you only posted nonsense I wouldn’t bother to mention it.

You might enjoy Hilbert’s hotel. Or then again, maybe this will only confuse the issue.

en.wikipedia.org/wiki/Hilbert%2 … rand_Hotel

No. Consider a variable x that ranges over the set {1, 2, 3}. Consider basic finite probability theory. The roll of a single six-sided die. You use variables to stand for things like “I roll a 3,” or “I roll and even number.” There is no implication of infinity.

No. What can you possibly mean by that?

Word salad. Makes no sense. I’m disturbed by the fact that I formerly thought you were making some level of sense in your posts, and now I wonder if I missed this strain of illogic. Can you put your morning flood of posts into context? It all seems … well, not good.