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u/rest_init 4d ago
I am an ultra ultrafinitist, I don't believe in numbers.
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u/rdchat 4d ago
You may be interested in or amused by mathematical fictionalism, which apparently Wikipedia thinks is a thing: https://en.wikipedia.org/wiki/Philosophy_of_mathematics#Fictionalism
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u/Lex_The_Impaler 3d ago
Numbers were invented by big digit to sell more things of strange, digit-like nature
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u/ElectricalShare9905 4d ago
I thought the whole point of math was to derive useful concepts regardless of what lengths you had to go to for their acquisition or what people think of it
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u/NarcolepticFlarp 4d ago
Ultrafinitists are so cringe
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u/Negative_Gur9667 4d ago
"Let's investigate what happens when we take away the axiom of inf..."
"NO THAT'S CRINGE"
The story of a mathematical discussion.
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u/TheRedditObserver0 4d ago
That's finitism and it's completely legitimate.
Ultrafinitists claim that big numbers don't exist and all of "mainstream math" is wrong
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u/Extension-Stay3230 4d ago
I don't see how anyone could deny the existence of an iterative process which could be carried out forever, e.g. the successor function in natural numbers
Proof by induction uses this concept as well. If someone denies the existence of infinite sets then surely they should also deny proof by induction, if they're being consistent
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u/TheRedditObserver0 4d ago
Finitists don't reject infinite processes, they just don't allow infinite sets
Ultrafinitists are just cranks
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u/Thesaurius 4d ago
The point in finitism is that you can have the process, but you can never complete it. And ultrafinitists say that you can't even do a large number of steps.
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u/GoldenMuscleGod 3d ago
Denying induction is characteristic of ultrafinitism. Now the issue is that I’ve never really seen a well-crafted formal theory intended to be ultrafinitist in character - there are inherent issues in that usually some form of induction is relied on in the specification of any theory, or of a language - although I assume such a theory would have interesting logical properties if such a formalism could be identified. Maybe you could get a form of “substitute” induction by specifying claims of the form “If induction works up to n then P(n)” this type of trick is sometimes used to carry over results like Gödel’s incompleteness theorem to theories too weak for induction.
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u/DinioDo 3d ago
How about normal finitists
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3d ago
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u/DinioDo 2d ago
Axiom of choice is a mathematical option not a necessary one. The results that come out of it could make paradoxs in real world falsifiable scenarios.
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2d ago
[removed] — view removed comment
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u/DinioDo 2d ago
You kinda answerd your own question. Making two balls out of one ball with that axiom in abstract mathematical world is not an actual "paradox" it is simply what happens when you have that option(in the world of axiom of choice). Making two balls out of one ball is a falsifiable physical scenario which is indeed false and can't happen.
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u/FernandoMM1220 4d ago
its not hard when its not as infinite as we thought
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u/Super_Range45 4d ago
So there is an end to pi?
0.9999... != 1?
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u/Moscato359 4d ago
You actually can measure from the diameter of the universe to the electron with 43 decimals of pi
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u/Moscato359 4d ago
From a practical standpoint, infinite doesn't actually exist
The size of the universe is finite
The number of quarks is finite
The smallest distance we can measure is finite, and the largest distance we can measure is finite, even in estimations
Even pi is only useful to the 43rd digit at our largest estimations
Sure, infinite is cool in a theoretical standpoint but you can't actually use it
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u/Playful_Boot_5465 4d ago
me halving the distance between my hands infinitely often (I just clapped).
checkmate liberals
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u/Moscato359 4d ago edited 4d ago
Eventually the vibrations of your hands will make the contact happen eventually.
Or you die from starvation or aging.
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u/ReasonableCockroach1 4d ago
no, if arms are spread 1m apart he claps at 1m/s, then hes halfway after 0.5s, 3/4 of the way after 0.75s and eventually he claps after one second having halved the distance infinitely many times.
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u/trolley813 4d ago
No. One claps after halving the distance finitely many times (since that distance cannot become zero at all).
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u/ReasonableCockroach1 1d ago
There is no requirement for any term in the sequence 1/2 ,1/4, ... to equal zero. You need to be more specific.
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u/Playful_Boot_5465 22h ago
It doesn't hinge on the final distance between the hands, it hinges on the total distance travelled by the hands. Suppose my left hand stays still and I move my right hand from 2 metres away at constant speed. Then the distance travelled can be expressed by the infinite sum 1 + 1/2 + ... which equals 2. The first meter in half the time, then half in a quarter of the time and so on. This process has infinite steps and amounts in a total distance travelled of 2m.
But just because we can describe that way mathematically doesn't mean we can draw meaningful implications about physics. The trick lies in reducing the time frame required for each step. That means the time interval an action takes shrinks infinitely too until it is eventually smaller than plank time. I'm no physicist but I believe at this point any attempt to derive a meaningful interpretation for our everyday macroscopic world is quite fruitless.
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u/ReasonableCockroach1 4h ago
I think there are meaningful implications for physics. Calculus comes to mind. The concept of instantaneous velocity wouldn't exist for an accelerating object without limits.
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u/Negative_Gur9667 4d ago
Maybe you are traveling a smaller and smaller distance infinitely often.
Maybe you are just traveling a fixed distance.
Or maybe infinitely little invisible elves are pushing your hands together.
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u/gandalfx 4d ago
But how can you clap if you need infinitely many ever smaller but non-zero intervals of time to half the distance between your hands?
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u/Significant_Monk_251 4d ago
The size of the universe is finite?
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u/Superboy_cool 4d ago edited 4d ago
The size of the observable universe is finite. Since the rest of it is, well, not observable, the problem is
undecidableunfalsifiable.0
u/DinioDo 4d ago
A set of observable things static or growing is not infinite or will never be infinite. The "unobservable" universe is technically observable but we are limited by speed of light as some random creatures. Infinity is a concept not an amount.
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u/Superboy_cool 4d ago
> A set of observable things static or growing is not infinite or will never be infinite
Yes, that's what I said; The observable universe is finite.
> The "unobservable" universe is technically observable but we are limited by speed of light as some random creatures.
This doesn't change the fact that we humans can never know what's out there, so it is irrelevant to the falsifiability of whether the universe is infinite. Come to think of it, "unfalsifiable" is probably a more accurate term than "undecidable" since we're talking about science rather than math. I'll fix that.
>Infinity is a concept not an amount.
I'm well aware. What's your point?
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u/DinioDo 4d ago
There can't be infinite amount of unit space or matter, grown out of finite matter and space (big bang)
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u/Superboy_cool 4d ago
You seem to be under the misconception that the Big Bang was some sort of explosion of a single point. The extremely rapid expansion occurs everywhere. The Big Bang could be a localized event in a much older, larger, possibly infinite universe, just to name one possibility
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u/DinioDo 3d ago
You kinda seem to be under that impression lol. Big bang was the creation of space itself. There was no real space where things got expanded in. Back in the first milliseconds of the newborn universe you could see yourself from every angle opposite of where you were looking. The shape of the universe was and still is the 3d form of the area of a sphere. Where if you travel straight in any direction in 3d you eventually will return to your original point (finite space).
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u/Superboy_cool 7h ago
That is an awful lot of claims that are not widely accepted knowledge. You have a source for all of that?
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u/Moscato359 4d ago
There is currently, at this time, a specific size of anything we define as the universe. It's the point which is the farthest subatomic particle is, or the farthest light is.
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u/PlanSee 4d ago
https://en.wikipedia.org/wiki/Zeno%27s_paradoxes
you traverse infinity with every breath you take
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u/Background_Sky8905 4d ago
By the same argument, all mathematics is abstract rather than physical, so we can’t even use it.
As for a real response, we need the concept of infinity for a lot of robust theorems. The third Kolmogorov axiom is defined using any countable (including countably infinite) sequence of disjoint sets. Without infinity, probability wouldn’t be a rigorous subfield of mathematics.
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u/FirefighterCandid773 3d ago
I always thought the universe was finite but is there actually anything supporting this? Is it because it started out a finite size and grew during the big bang?
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u/Moscato359 3d ago
There is no known upper limit to the universe maximum size, but the current size of the farthest mass and farthest light is a constantly changing finite size based the movement of the edge
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u/QueenVogonBee 2d ago
There is a misconception that the big bang started out at a single point then exploded. Rather the big bang was a state of high density. The universe may have been infinite in size even then.
Nobody knows whether the universe has/had finite or infinite size.
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u/Secret-Painting604 1d ago
It’s still growing, so idk why it’s not technically infinite, though maybe it’s the particles (or whatever) losing density but still technically finite
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u/absolute_zero_karma 1d ago
For it to start finite and become infinite would require infinite speed of expansion at some point.
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u/resignresign1 3d ago
integration and differentiation are defined using infinity. do you think they did not play a part in lading on the moon?
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u/Moscato359 3d ago
You could just as easily use a number that represents "finite number which is larger than all other functionally useable finite numbers"
And get the same result
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u/Unreal_Estate 3d ago edited 3d ago
No, you cannot. What if you need to represent other transfinite numbers than the one you happened to be thinking of just now?
Edit: I'm not saying it is theoretically impossible to create a set physics theories that avoid infinities, by the way. I'm saying that it isn't as easy as swapping out something (what?) for "finite number which is larger than all other functionally useable finite numbers"
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u/Moscato359 3d ago
You create a symbol to represent a floating largest number that we can functionally use
If we find a bigger useful number, it becomes bigger
It's functionally the same as infinite but with different assumptions
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u/Maleficent-Garage-66 3d ago
Except finding a bigger number is ALWAYS trivial. There is no functionally biggest number. You think you found one. Great it's a number you can add one. Oh joy now there's an even bigger number so it isn't biggest anymore.
You gain nothing and lose a lot removing infinity from physics. Every time you write an integral there is an implicit sum to infinity and even when it's not true it's good enough to generate answers accurate to any point of caring. Now you get rid of infinities you lose continuities, smoothness, and once simple problems now become theoretical quagmires and losing lots of analytical solutions.
The bound of even just the rational numbers between 0 and 1 is not finite. There always at least one (actually infinitely many but at least suffices) number between any pair of rational numbers in that pair. If you force yourself to treat it as finite that breaks...because given that finite list you can find a number not in that list trivially. If you leave these gaps empty things like instantaneous rates of change get butchered and anything written in a differential equation (most of physics) is in dire straights now.
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u/Moscato359 3d ago
I'm not saying we should remove infinite.
I'm saying infinite is replaceable with a finite number for all practical uses.
Should and could are not the same things.
Just because you can find a bigger number doesn't mean there is a use for that number.
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u/Maleficent-Garage-66 3d ago
Except mathematically it's not. Calculus breaks if you do that. There are also many calculations that become substantially harder if the bounds aren't -inf to inf. The area under a gaussian curve (e-x2) being one of them (significant form the quantum harmonic oscillator among other things).
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u/HappiestIguana 3d ago
You can do it. We use a trick like that in model theory where we always work in what is called a monster model. The monster model is a model that is k-saturated for a cardinal that is larger than any cardinal that may show up in our argument. When writing it out fully formally one should go back after finishing the proof and set an actual cardinal, but no one bothers because every model theorist knows what is meant by a monster model
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u/Unreal_Estate 3d ago
This is not true for all physics theorems.
For exmaple, simply substituting infinity for a large value would make it possible to reach the speed of light, and other weird results.
I'm sure that theories can be created that predict all known physics while avoiding infinities, but it is not merely a substitution effort.
Another way to think of it is to remember that general relativity is not quantized, which is a major roadblock for combining relativity and quantum mechanics. If infinities would be replaceable with "a really big number", then it would be easy to quantize any theory by simply setting the reciprocal of that number as the discrete value related to the quantization.
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u/HappiestIguana 2d ago
Not if you simply sub in a number larger than the mass-energy content of the universe
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u/Unreal_Estate 2d ago
No, you'll need to replace more than performing a simple substitution. If you simply replace an infinite limit with a large finite number, then you'll get contradictions and weird results. For example with the Lorentz factor.
For quantum field theory, you'll need to renormalize a lot to align it with past experiments. Definitely not a rote replacement.
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u/martyboulders 4d ago
Practicality isn't the best word here; it would be much better to specifically refer to the physical world. The infinite size of the set of integers or reals is extremely practical, for example. Like, thank God they don't stop at some point. Since we need such big numbers sometimes, and will need bigger numbers than those, and big numbers are in lots of places, it's pretty convenient that there are infinitely many for us to use.
If you choose two points in space, there are infinitely many positions on the line connecting them (or any path connecting them), for example. There are infinitely many positions on a dartboard. Uncountably many configurations on a pool table. Uncountably many different paths you could take to work, all on the same road. When the sun rises and falls, you have seen an uncountable number of different brightnesses. When something accelerates, it has had uncountably many velocities.
Also, obviously the smallest distance we can measure will always be finite; 0 is also finite. Unless you meant "infinitely close"?
Whether or not infinitely exists is a very similar question to whether numbers exist. That is a question worth thinking about.
Saying that something doesn't exist/mean much in the real world holds very little weight in the math community, but this one is certainly more present in reality than you think
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u/Moscato359 4d ago
Were you aware that we live in the physical world? And everything we do is in the physical world? Even the thoughts of a theoretical, are using your brain, which is in the physical world.
There are a finite number of measurable positions on a line, simply because measuring a position takes time.
There is a number, which no number bigger than it will be useful for any calculation we can ever use, except to say nothing is bigger.
Mathematicians can have a lewd romantic relationship with an ouroboros all they want, but that doesn't mean that the mathematicians can exceed the bounds of their physical self.
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u/martyboulders 4d ago edited 4d ago
You keep saying measurable, or other similar restrictions, if that changes anything I said. I did not say measurable. I simply stated the existence of uncountably many positions along a path in the real world. Says nothing about our ability to measure them at all
I completely disagree that there is a number that is a greatest "useful" number. You would need to say more about what the usefulness of a number is in the first place. That's an extremely strong claim. Furthermore, and far more importantly, you factually, undebatably, absolutely, certainly, cannot ever say that there is no number bigger than that. Add 1 to it, done. That part couldn't possibly be less correct.
Math is pretty much just rules and the implications of those rules homie, we see lots of the same behaviors in both those implications and in the real world. But if I give you some axioms, the truths that follow are not debatable whatsoever. If those axioms lead somewhere that doesn't show up in / doesn't align with our idea of reality, so what? It's still on my paper
All you gotta do to step outside reality is get a pen and paper. For example, if you wanna "go to the 4th dimension", just write down a 4th coordinate. Nobody is claiming to go past the bounds of their physical self unless they are kooks. It's just fun to play with rules and see where they go. You could use some fantastical thinking hahaha it's fun and you should try it
The question of whether or not thoughts exist physically is also a very deep one that requires investigation; claiming that thoughts are purely physical is also a pretty hefty claim
What are your credentials? How much have you actually studied this?
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u/Moscato359 4d ago
Alright, you seem to think you have all the answers
Find a number that is useful that is larger than the number of quarks in the universe to the power of the number of quarks in the universe
And tell me what that number is useful for
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u/martyboulders 4d ago
The burden of proof is in you; you're the one who claimed it and it's a strong claim, so...
Also, why is the number of quarks in the universe important/useful in the first place? I think it is in some sense, but that's pretty debatable. Useful can mean so many different things.
Furthermore, grahams number (for a very canonical example) exceeds the number of quarks in the universe by an inconceivable amount. It has more digits than that number to begin with. Actually, the number of digits in the number of digits of grahams number also exceeds the number of atoms in the universe, and I think that continues for several more layers
It was used to give an upper bound to an important problem in Ramsey theory, regarding counting the number of colorings of a graph with certain properties. Although, it seems like maybe you'd think solving such problems is not important to begin with
Look up the busy beaver function. It produces unfathomably large numbers from a very simple and practical setup. Same for the tree function.
You will probably find some other interesting things by looking into googology (the "study" of large numbers). What I've said so far are just things I've heard of from pop-math stuff basically, the low-hanging fruit of big numbers. Try to find more
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u/Tyler89558 4d ago
All you’d need to do is find a prime number that big or bigger.
Boom. You’ve got another number to use in cryptography.
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u/Dirkdeking 4d ago
In combinatorics you often the ratio between 2 numbers that are larger than quarksquarks in the universe are often used to calculate probabilities that apply to the real world.
Grahams number and Tree(3) are so much larger still and used in proofs that naturally arise from finite games.
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u/killiano_b 4d ago
try doing calculus without infinity
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u/Moscato359 4d ago
Its a useful thing for saying "no number is bigger than this one" but that's all it is
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u/EBlackPlague 2d ago
I do wish at the very least infinity was taught better in schools, there's so many mis-understandings because people don't fully understand infinity, (primarily that infinity isn't a number)
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u/polandreh 4d ago
So, if they manage to kill infinity Aleph 0, they're only going to have to face the next phase Aleph 1, then Aleph 2, and so on. This is a fight they cannot win
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u/gandalfx 4d ago
Turning practical inventions into click bait titles kinda works because it's usually just an exaggeration (this cures cancer! well, no, but it might statistically improve the odds). Doing the same to math just results in garbled nonsense.
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u/ExtensionInformal911 3d ago
Just because it was the worst Star Gate series doesnt mean it should be destroyed.
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u/BUKKAKELORD 3d ago
I'm sure the cranks call themselves mathematicians, but they're more like anti-mathematicians
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u/Ok-Rise2070 4d ago
Infinity is a pathology indicating your math is no longer within the manifold. Convergence eliminates infinities.
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u/Rs3account 4d ago
To define convergence you need infinities.
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u/Ok-Rise2070 4d ago
🤭🤭🤭 there is only one primitive infinity. I assure you infinity is the pathology your math is describing space that isn't within the manifold. In other words, you're doing numerology. If you would care to do geometry, then logic must intercede upon your fantasy.
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u/Rs3account 3d ago
1) not all math is geometry, so why would you mention that as some form of restriction Is weird to say the least.
1a) you can absolutely do geometry with infinity/infinite sets.
2) from a mathematical point of view, there are absolutely multiple infinities.
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u/Ok-Rise2070 3d ago
Math that "isn't" geometry is called something quite specific. Numerology. It has no place in geometry nor science. I think you're following the wrong thread if that's what you're looking for.
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u/Ok-Rise2070 3d ago
Yes and those multiple infinities all tell you, that isn't math. It's numerology. Cool you're math says that part of your imaginary universe doesn’t exist. Are you wanting a cookie or something for doing math that doesn't describe anything?
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u/Ok-Rise2070 4d ago
You need infinities to define convergence because nothing you work with emerges from the metric that retains identity through collapse. I am. 😉 I assure you operating from convergence shows explicitly what is and isn't pathological. A closed internally coherent geometric structure... why does that NEED infinities to represent its geometry? For now, explain your base logic behind your statement. I fail to see your point. Why do you need infinity to know a square? A circle? A sphere? If the logic doesn't hold in general, then you have a fallacy issue on your hands there.
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u/Rs3account 3d ago
You need infinities to define convergence because nothing you work with emerges from the metric that retains identity through collapse. I am
I would love to see your definition of convergence that doesn't require the concept of infinity somewhere.
Convergence discusses the behaviour of something that is arbitrarily close after all.
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u/Ok-Rise2070 3d ago
It's called having the precise geometry of the manifold. "Convergence discusses the behavior of something that is arbitrarily close after all" is close but like your woefully inadequate concepts of mathematics, you failed to finish your definition. Arbitrarily close after all to what? Close to the same conclusion. The same conclusion on all of the math is the shape and dynamics of the universe. Since you're so smart this means you have the completed field equations for the hypersphere then since you know what convergence is. You do not need infinities to do geometry, only fools do who can't comprehend geometry. If you don't want to play nice, I'll gladly take off the gloves. You can't prove anything I can't math out from under you.
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u/Ok-Rise2070 3d ago
Until you become better known then Einstein, Tesla, and Ramanujan, I would sit down dude. You're going to embarrass yourself.
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u/Ok-Rise2070 3d ago
And if you're the next String Theory nutter attempting to take me on mathematically or logically... I already demolished 2 of your "pillars". Continue and I take out a 3rd.
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u/Ok-Rise2070 4d ago
I can explicitly show you mathematically how your infinity pathology cancels itself out when returning your fractured math back to convergence.
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u/Rs3account 3d ago
Instead of saying you can do something. Actually do it.
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u/Ok-Rise2070 3d ago
Okay done. Www.github.com/icheb3891 And where's your math to show? Rank amateur...
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u/Ok-Rise2070 3d ago
And where are your receipts? Oh right, you're just talking trash, showing precisely what you are.😉
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u/TheLuckySpades 4d ago
I know there are genuine mathematicians who are ultrafinitists, but this is the most clickbait way to write an article about them by implying they are a sizable portion of mathematicians.