/sci/ - Science & Math » Thread #11247677

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"""""""math""""""""

Anonymous Mon 23 Dec 10:53:53 2019 No.11247677 View Reply Original Report

Quoted By: >>11247682 >>11248420 >>11248651 >>11249689 >>11249800 >>11249821 >>11250175 >>11250211 >>11250871 >>11250932 >>11252315

>the sum of an infinite amount of things is equal to one thing
S = 0.9 + 0.09 + 0.009..... = 1

90% of of bread crumbs + 9% of bread crumbs + 0.9% of bread crumbs +.... = loaf of bread with finite volume

Yeah, I'm done with tbis shit. FUCK YOUR "MATH".

Anonymous

Anonymous Mon 23 Dec 2019 10:58:57 No.11247682 Report

Quoted By: >>11247685 >>11247723 >>11248633 >>11248701

>>11247677
I agree.
People keep insisting there are infinite number of dots on a number line between 0 and 1,when obviously the line is finite with start and end.
Some of those dots in between are difficult to compute but they are surely not infinite in count.

Anonymous

Anonymous Mon 23 Dec 2019 11:00:26 No.11247685 Report

Quoted By: >>11248674 >>11248829 >>11248836 >>11249727 >>11250854 >>11251404

>>11247682
There has to be a boundary where the counting stops, surely. Why isn't Planck length it?

Anonymous

Anonymous Mon 23 Dec 2019 11:41:23 No.11247723 Report

Quoted By:

>>11247682
The number line is a mathematical abstraction which does not derive from reality, and can only model it in some cases. We construct the number line so that it is ordered and we can do basic arithmetic on it, like division, addition, subtraction and multiplication. Just requiring these things, the line is then forced to be infinite, for between any two points we can take the mean and get a new point strictly in between them. If the line was finite, this would not be possible.

Anonymous

Anonymous Mon 23 Dec 2019 18:16:28 No.11248420 Report

Quoted By: >>11248441

>>11247677
>90% of of bread crumbs + 9% of bread crumbs + 0.9% of bread crumbs +.... = loaf of bread with finite volume
why would this not be the case?

>There has to be a boundary where the counting stops, surely. Why isn't Planck length it?
bait

Anonymous

Anonymous Mon 23 Dec 2019 18:25:47 No.11248441 Report

Quoted By: >>11248445

>>11248420
It's not bait. I literally want to know the answer to that.

Anonymous

Anonymous Mon 23 Dec 2019 18:27:30 No.11248445 Report

Quoted By: >>11248449

>>11248441
you seriously think "half the planck length" just isnt a thought? I'm thinking it right now.

Anonymous

Anonymous Mon 23 Dec 2019 18:28:26 No.11248449 Report

Quoted By: >>11248466 >>11248474 >>11248491

>>11248445
I thought the planck length was literally the smallest possible increment of reality?

Anonymous

Anonymous Mon 23 Dec 2019 18:33:50 No.11248466 Report

Quoted By: >>11253751 >>11254381

>>11248449
Mathematical objects arent in the physical world, they are in the mind/"platonic realm", these objects are extrapolations of our thought which extend far beyond what we perceive with our senses. If I can conceive of a number smaller then the unit measurement of the Planck length, then I can study this number and its properties as long as there is no contradictions. Infinity exists exactly because we conceive of it, ie the size of the natural numbers. Math belongs to pure thought, not science.

Anonymous

Anonymous Mon 23 Dec 2019 18:35:47 No.11248474 Report

Quoted By:

>>11248449
It is not. That's pop sci nonsense that took "known models of physics break down on the planck scale", played a game of telephone with it, and output "the planck length is the shortest possible length."

Anonymous

Anonymous Mon 23 Dec 2019 18:41:56 No.11248491 Report

Quoted By:

>>11248449
planck length is the smallest increment that is meaningful in our current mathematical models

Anonymous

Anonymous Mon 23 Dec 2019 19:47:33 No.11248633 Report

Quoted By: >>11248643 >>11250786

>>11247682
There certainly are. For every number on that line, I could add more digits to yield a new number. Therefore, there are infinitely many numbers there.

Anonymous

Anonymous Mon 23 Dec 2019 19:49:29 No.11248643 Report

Quoted By: >>11248655

>>11248633
Infinite != Indefinite. You silly undergrad.

Anonymous

Anonymous Mon 23 Dec 2019 19:50:46 No.11248651 Report

Quoted By: >>11248677 >>11250215

>>11247677
When we say that an infinite series is equal to some number, you're right in asserting that it's not strictly a sum definition. We take the number that the series converges to and assign it as the sum.

The more breadcrumbs you have, the closer and closer you will approach having that fininite loaf (without ever having it). For all intents and purposes, you have a finite loaf.

Anonymous

Anonymous Mon 23 Dec 2019 19:51:57 No.11248655 Report

Quoted By:

>>11248643
Enlighten me

Anonymous

Anonymous Mon 23 Dec 2019 19:57:04 No.11248674 Report

Quoted By:

>>11247685
Anon the plank length is a very very small number, if we stopped counting there we wouldn't have any numbers.

Anonymous

Anonymous Mon 23 Dec 2019 19:57:55 No.11248677 Report

Quoted By: >>11248707

>>11248651
.999... is exactly one though.

Anonymous

Anonymous Mon 23 Dec 2019 20:02:07 No.11248701 Report

Quoted By: >>11253747 >>11253751

>>11247682
Mathematics is more fundamental than physical reality

Anonymous

Anonymous Mon 23 Dec 2019 20:02:47 No.11248707 Report

Quoted By: >>11251409

>>11248677
0.abcd... is a notational shortcut for a set of equivalence classes of infinite cauchy sequence of rational numbers (all converging to the same point of the completion). Of course 0.999... is 1, but more precisely it is (abuse of) notation representing the limit of a sequence which converges to 1.

Anonymous

Anonymous Mon 23 Dec 2019 20:43:37 No.11248829 Report

Quoted By:

>>11247685
>muh Planck length meme
Stop reading popsci and get a real textbook

Anonymous

Anonymous Mon 23 Dec 2019 20:45:39 No.11248836 Report

Quoted By:

>>11247685
>length

Numbers don’t have to be represented in space

Anonymous

Anonymous Tue 24 Dec 2019 04:56:34 No.11249689 Report

Quoted By:

>>11247677
s

Anonymous

Anonymous Tue 24 Dec 2019 05:19:41 No.11249727 Report

Quoted By:

>>11247685
Planck Length is a physical term relating to the point that "distance" stops being meaningful. You can certainly count to numbers lower than it.

Anonymous

Anonymous Tue 24 Dec 2019 06:04:04 No.11249800 Report

Quoted By: >>11253770

>>11247677
Not only that is true but also things like $\forall A \subseteq \mathbb{R} \hspace{2mm} , \hspace{2mm} A \sim \mathbb{R}$
This fact follows from the nested interval property, which follows from the action of completeness, which states that ever bounded subset of the real numbers has a supremum.

Things like $\mathbb{Z} \sim \mathbb{N}$ are also true.

You should look into cardinality, its pretty interesting.

Anonymous

Anonymous Tue 24 Dec 2019 06:17:31 No.11249821 Report

Quoted By: >>11249837

>>11247677
You find yourself on a football (soccer) fields goalpost.

Youre told that if you can make it to the opposing goalpost, you automatically gain 1 billion dollars.

The catch, you can only advance half of the distance you have left, so on your first move you get to the midfield, on your second you get to 3/4 of the way, and so on.

How many steps do you need go take in order to get to the opposing goalpost?

Anonymous

Anonymous Tue 24 Dec 2019 06:23:16 No.11249837 Report

Quoted By: >>11249844

>>11249821
infinite, the trick is to do the steps infinitely fast

Anonymous

Anonymous Tue 24 Dec 2019 06:26:44 No.11249844 Report

Quoted By:

>>11249837
Just do each one twice as fast as the previous one.

Anonymous

Anonymous Tue 24 Dec 2019 11:44:01 No.11250157 Report

Quoted By:

This whole thread is one massive bait. The pic alone should be a red flag to all of you.

Anonymous

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Anonymous Tue 24 Dec 2019 12:02:43 No.11250175 Report

Quoted By:

>>11247677
this guy is an attention whore.
Nelson was a more humble and wise ultrafinitist

Anonymous

Anonymous Tue 24 Dec 2019 12:42:08 No.11250211 Report

Quoted By:

>>11247677
stop associating yourself with wildberger you fucking brainlet

Anonymous

Anonymous Tue 24 Dec 2019 12:45:13 No.11250215 Report

Quoted By:

>>11248651
>We take the number that the series converges to and assign it as the sum.
The finite sums within the series converge to it. The series itself doesn't converge but is equal to it.

Anonymous

Anonymous Tue 24 Dec 2019 18:32:55 No.11250786 Report

Quoted By: >>11250952 >>11250973 >>11257244

>>11248633
I don't think that's true because each number has to have a symbol associated with it but if you continue to find a point in between each pair that you choose until you've done this a number of times that is equal to the number of particles in the universe then in order to define the number in between the two you are left with, you would need to break the laws of physics, which means that even if you claim it exists you can never define it which means there are a finite number of points on the line segment

Anonymous

Anonymous Tue 24 Dec 2019 19:12:01 No.11250854 Report

Quoted By:

>>11247685
brother this doesn't make any sense

Anonymous

Anonymous Tue 24 Dec 2019 19:18:29 No.11250871 Report

Quoted By:

>>11247677
Norman would agree with you: if you have bread, and you cut off 90%, and then you cut off 90% from the smaller piece, and so on, then it means that you had less bread when you started than you actually had.

Anonymous

Anonymous Tue 24 Dec 2019 19:53:01 No.11250932 Report

Quoted By:

>>11247677
When you walk one meter, you first walk a half meter, then you walk a quarter meter, then you walk an eighth meter etc. How could you possibly walk a whole meter when you have infinitely many increments to cross? Because of convergence, that's why, and it's for exactly the same reason 0.99... = 1.

Anonymous

Anonymous Tue 24 Dec 2019 20:07:14 No.11250952 Report

Quoted By:

>>11250786
>each number has to have a symbol associated with it
Why would you think that?

Anonymous

Anonymous Tue 24 Dec 2019 20:18:26 No.11250973 Report

Quoted By:

>>11250786
The laws of physics don't apply; a number line is an abstract concept.

Anonymous

Anonymous Tue 24 Dec 2019 23:34:33 No.11251404 Report

Quoted By:

>>11247685
Not only that what other anons said, but, as an actual astrophysics PhD of a reputable uni told me in a talk, the Planck length is only a thing now because we don’t have an accurate enough theory of quantum gravity.
Drop the pop sci

Anonymous

Anonymous Tue 24 Dec 2019 23:36:43 No.11251409 Report

Quoted By: >>11253730

>>11248707
Nicely said. 0.999 doesn’t equal 1 intuitively, doesn’t matter how close you get, you’ll never get to 1 if you don’t add that 0.000...1 at the end

Anonymous

Anonymous Wed 25 Dec 2019 00:15:28 No.11251554 Report

Quoted By:

https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/real.pdf

Anonymous

Anonymous Wed 25 Dec 2019 00:23:42 No.11251579 Report

Quoted By: >>11252319

Hypothetically speaking, if the shortest length in reality is the planck length, what would that even mean. Does that mean matter snaps to a 3D grid where the grid points are spaced by planck lengths?

Anonymous

Anonymous Wed 25 Dec 2019 04:35:40 No.11251975 Report

Quoted By:

>let me impose my physical intuition into what is ultimately abstract concepts.

Hoaxfag

Hoaxfag Wed 25 Dec 2019 05:03:52 No.11252012 Report

Quoted By:

You need to use asymptotes to graph this,
Planck length is for the infinitely small.
This is the infinitely big (approaching infinity)
The asymptote lies at the limit of 1
1 is the limit of this equation,
0.999... gets closer and closer to 1 forever , but it never reached one.

The Planck length limit lies at 52 decimals, if you calculate pie to 52 decimals with the circumference being the size of the observable universe , it allows you to calculate measurements of less than a hydrogen atom, so any more decimals is pointless,
So an symptoms also lies just before 0 in the other direction, the asymptote of mesurement is at just before 0, you cannot measure any l as than 53 decimals of pi, so that's where the asymptote lies.

Anonymous

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Anonymous Wed 25 Dec 2019 09:57:21 No.11252273 Report

Quoted By:

>infinite transcendental "real" numbers
>only 2 (two) are relevant/useful

Anonymous

Anonymous Wed 25 Dec 2019 10:26:02 No.11252315 Report

Quoted By:

>>11247677
>I don't understand it, therefore it is bullshit
Rid earth of yourselves, brainlets.

Anonymous

Anonymous Wed 25 Dec 2019 10:28:28 No.11252319 Report

Quoted By:

>>11251579
no, everything can move over 1/100 of a planck length and nothing will change.
the planck length is just the closest distance you can calculate effects of a particle with its surroundings. that is, with current physics formulas.
once QFT and GR get merged, it might be possible to calculate closer than the planck length.

Anonymous

Anonymous Wed 25 Dec 2019 23:24:28 No.11253730 Report

Quoted By:

>>11251409
aren’t 0.9999... != 1 threads worthy of bans?

Anonymous

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Anonymous Wed 25 Dec 2019 23:29:07 No.11253739 Report

Quoted By:

pic related has finite volume but infinite surface area

Anonymous

Anonymous Wed 25 Dec 2019 23:33:09 No.11253747 Report

Quoted By:

>>11248701
>Mathematics is more fundamental than physical reality
/x/

Anonymous

Anonymous Wed 25 Dec 2019 23:35:24 No.11253751 Report

Quoted By: >>11255648

>>11248466
>>11248701
>Mathematics is more fundamental than physical reality
/x/
>Mathematical objects arent in the physical world, they are in the mind/"platonic realm"...
Occultist nonsense belongs in /x/

Anonymous

Anonymous Wed 25 Dec 2019 23:45:41 No.11253770 Report

Quoted By:

>>11249800
You need to refine that statement. $\mathbb{N} \subset \mathbb{R}$ but they are not isomorphic.

Anonymous

Anonymous Thu 26 Dec 2019 04:45:38 No.11254381 Report

Quoted By:

>>11248466
platonism is fine but I dont give a shit you still have to define the bread in physical terms or switch to a mathematical description

Anonymous

Anonymous Thu 26 Dec 2019 21:50:01 No.11255648 Report

Quoted By:

>>11253751
The nonsense is denying objective reality because of a low IQ incapable of understanding anything but the physical subset of total reality
If your position is actually "math isn't real!" then you belong to /x/

Anonymous

Anonymous Fri 27 Dec 2019 14:23:07 No.11257188 Report

Quoted By:

I've always thought it as an imaginary play, not an attempt to understand the real world.
Of course that doesn't mean our current definition of maths is perfect, there is much to be improved upon. But it doesn't need to be based in real world?

Anonymous

Anonymous Fri 27 Dec 2019 14:30:18 No.11257204 Report

Quoted By: >>11257223

i watched a new wildberger video recently and saw that he's touting his new field of "chromogeometry" what a fucking fame whore. there's not an original thought in his brain.

Anonymous

Anonymous Fri 27 Dec 2019 14:53:34 No.11257223 Report

Quoted By:

>>11257204
Just wait till you see the next step up: "monochromogeometry".

Anonymous

Anonymous Fri 27 Dec 2019 15:07:19 No.11257244 Report

Quoted By:

>>11250786
You stopped arguing about points on a line and instead tried to argue that there isn't a valid idea of infinity merely because what we experience tends to be finite, by some arbitrary measure of "particles". Why then would anyone call anything infinite? Why is it that infinity remains to be an understandable, and ultimately a useful and pragmatic concept when talking about mathematical things, when, by your argument, it's not actually possible for something to be infinite, even hypothetically?
How many numbers are there? Only as many as there are particles in the universe? If you say so, sure, but that's a different axiomatic paradigm from the one that mathematicians and physicists used in the first place to discover your precious particles.
Fucking nigger.

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