Proof of Finitism

[Anonymous No.15912121]

Consider the set of fractional numbers between 1 and 2.

The members of the set of fractional numbers between 1 and 2 simultaneously add up to 1 (since they're the amount 1 and 2 are separated by) and to ∞ (since they are all positive and greater than zero, and the infinite addition of positive numbers greater than zero equals infinity), a contradiction meaning:
1 = ∞

We can do the same for all numbers (numbers between 1 and 501 for instance to get
500 = ∞

And if we can prove both
1 = ∞
and 500 = ∞
then we can prove 1= 500

QED infinities yield contradictions and finitism is true

[Anonymous No.15912133]

>>15912121
Check this out. I can use your theorem prove that imaginary numbers exist and that they are perpendicular to real numbers:
8 = ∞

[Anonymous No.15912158]

>>15912133
First time I've laughed on /sci/

[Anonymous No.15912370]

Infinity is not a member of the reals

[Anonymous No.15912377]

>>15912370
What would you say the importance of this is on regards to what's said in the OP?

[Anonymous No.15912383]

ℵ0 and ℵ1 are distinct

[Anonymous No.15912393]

>>15912383
How would you say that impacts the OP argument?

[Anonymous No.15912396]

>>15912393
The infinities you are talking about are not the same- they have different cardinalities

[Anonymous No.15912401]

>>15912121
What the fuck are you on about?
>The members of the set of fractional numbers between 1 and 2 simultaneously add up to 1
They don't.
>(since they're the amount 1 and 2 are separated by)
No, that will be [that set] - 1
>and to ∞ (since they are all positive and greater than zero, and the infinite addition of positive numbers greater than zero equals infinity),
That would be the size of that set, and the sum of that set, is by definition, infinitely adding 1.(whatever) an infinite number of times. You're re-adding 1 over and over plus the decimals.
>a contradiction meaning: 1 = ∞
Does not follow.

The rest of your post is built on the same retardation.

[Anonymous No.15912409]

>>15912121
>The members of the set of fractional numbers between 1 and 2 simultaneously add up to 1

This is wrong. And you don't need infinity to see that it is wrong. e.g. 1.1+1.9 = 3. Already that's way more than 1, and I've only added up two members of your set. There's no reason the sum of the members should equal the difference of the set boundaries.

[Anonymous No.15912423]

>>15912396
Describe, in detail, how you believe that impacts the argument in the OP.

[Anonymous No.15912426]

>>15912401
>They don't.
They must. They are what bridges 1 and 2. So we have for instance the 0.5 and the 0.5 between them and added to 1 these get 2. We have the 0.25 the 0.25 the 0.25 the 0.25 between them and added to 1 these get 2. And so on.

>You're re-adding 1 over and over plus the decimals.
You've misunderstood what I mean by "the fractional numbers"
I.E. one member of the set of numbers between 1 and 2 is 1.25, and so in this case we'd be looking at .25

You can do the same with the numbers between 0 and 1 if it makes it easier to picture.

[Anonymous No.15912429]

>>15912409
>1.1+1.9 = 3
Like above you've misunderstood what I mean by "the fractional numbers"
I.E. one member of the set of numbers between 1 and 2 is 1.25, and so in this case we'd be looking at .25

You can do the same with the numbers between 0 and 1 if it makes it easier to picture.

[Anonymous No.15912452]

>>15912121
They don't add to infinity, though, because the numbers you're summing get infinitesimally small.

[Anonymous No.15912472]

>>15912426
Non sequitur. 1.25, 1.5, and 1.75 (after you've extracted the fractional bits) sum to more than 1.
For sums with vanishingly small terms, take the summands of the harmonic series (+1), which are rationals in that interval. The sum diverges. Or, to put it concretely, you can find a greatest integer smaller than any partial sum.

[Anonymous No.15912481]

>>15912133
fpbp

[Anonymous No.15912483]

>>15912121
OP is confusing cardinality and topology.

[Anonymous No.15912485]

>>15912121
You have to be 18 to post here

[Anonymous No.15912501]

>>15912429
But then .1+.9+.2+.8 = 2. You can generate pairs of "fractional numbers" that sum to 1, but so what? You can also generate pairs that sum to less than 1 (e.g. 0.1+0.2 = 0.3), and you can generate pairs that sum to more than 1 (e.g. 0.9+0.8 = 1.7).

[Anonymous No.15913355]

>>15912452
Weirdly you actually do
Taking the fractional numbers all the way, the distance between 1 and 2 is 1/∞ added an infinite number of times
But any positive number added an infinite number of times gets ∞
So it HAS to be 1 and it HAS to be ∞, hence the contradiction

[Anonymous No.15913356]

>>15912501
The distance between 1 and 2 could be written as one half plus one half, or one quarter plus one quarter plus one quarter plus one quarter, or one-eitgth plus itself eight times
Following this you get one divided by infinity added it itself infinite times, which you can prove equals anything since the distance between say 0 and 2 gets this same result also, allowing you to prove 1 = 2

[Anonymous No.15913362]

>>15912472
You're starting to see the issue. It both must and must not have a finite total

[Anonymous No.15913363]

>>15912483
Demonstrate this

[Anonymous No.15913396]

>>15912121
I’m a finitist but this thread is retarded. Finitism is better because it’s more useful and doesn’t waste time on unfalsifiable nonsense. Simple as. We can still use limits and potential infinities etc., but undefinable numbers and uncountable sets and all the infinity paradoxes are bullshit

[Anonymous No.15913402]

>>15913396
You'll never get through to Infinitists that way, many many many of them are convinced that because infinity is a useful mathematical fiction that it not only can but does exist in the real world.

I've heard them say a black hole's "infinite density" falsifies Finitism and other such massive confusions

To those seduced by the lazy eight we must bring the light of the finite

[Anonymous No.15913411]

>>15913402
> infinity is a useful mathematical fiction
But it’s not. No real-world advantage has ever been obtained from actual infinities in math.

[Anonymous No.15913435]

>>15913411
They can never understand the difference...they'll talk about limits in calculus as if they're actual infinities because they see the lazy eight symbol

[Anonymous No.15913439]

>>15913435
Yes I’ve noticed that. They think that because we use limits (which existed long before Cantor and were used by Gauss who stated that we should never accept actual infinities, only potential infinities), then we must also have undefinable numbers and different sizes of infinity and blah blah blah

[Anonymous No.15913449]

>>15912121
OP is having fun but let's imagine that numbers are "expensive" to conceptualize, according to their size. 10 is cheap, 1000 is somewhat less cheap, but can you afford to think about 9997^(45678^12345) (or even its digit list in ten base)?

[Barkun No.15913452]

>>15913439
There's a logos in Starfield in the bottom left. It's the logo (to a certain degree of) the successful trick you do using matter if this image is a symbol of what matter is. Use the ability of the ship in Starfield to determine what the route of it is. Ask it what matter is as depicted by the image and then how it is the successful route to a trick using matter. Then ask if the question what is the vertical pinned trick that I know which is a while lot better, then ask it wants the swirling one along the same vertical route - all using matter.

[Barkun No.15913454]

>>15913452

[Barkun No.15913458]

>>15913454
Let's put it this way. The prophecy you gained from this simulation, has many different evolutions. There is a statue, a predatory Statue (you), an intellectual statue, an Astronomal statue, etc. the trick I know is the final form. try use the ship in Starfield to determine what statue you are and the matter trick to quickly create you as if there was a quick method.

[Barkun No.15913462]

>>15913458
Think: it's the 'logo' of the successful predator statue trick, what is its degree in comparison.

[Anonymous No.15913467]

>>15913355
That's just not true tho. An infinite series can converge to a finite value.

[Anonymous No.15913524]

>>15913467
With actual infinities it's always "it does this but it also does that mutually exclusive thing".
Like in the OP: under an Infinitist understanding the distance between any two numbers is a series of infinitesimals, which adds up to infinity and to the next number and to whatever else you want

[Anonymous No.15913541]

>>15913355
>But any positive number added an infinite number of times gets ∞
https://en.wikipedia.org/wiki/List_of_mathematical_series

[Anonymous No.15913563]

>>15913541
Tell me: what positive nonzero number added infinitely results in a number besides ∞?

[Anonymous No.15913614]

>>15913435
Explain formally what a limit is, without implicitly or explicitly referencing infinite sets such as N, Q, or R. Make sure to remember that there is no such thing as a finite set whose elements can get arbitrarily close to zero.

[Anonymous No.15913625]

>>15913614
We can still work with infinite sets. They’re just potentially infinite and not actually infinite. We could even assume that a set like N is finite, but it is so large that we have no idea where it ends. If the universe is finite, then N is necessarily finite (because they are NATURAL numbers). And even if the universe is infinite, then we still don’t have an infinite mind that can grasp infinite numbers.

[Anonymous No.15913630]

>>15913625
Not a formal definition, try again. Infinitists (i.e., real mathematicians) can do this effortlessly btw.

[Barkun No.15913632]

>>15913630
It's alright if you have no choice. Just try your hardest. Getting banned from here ain't much. I'll be on Twitter. Well make this better.

[Barkun No.15913635]

>>15913632
It's what it is, morally. You should get this. You're clean and good.

[Anonymous No.15913640]

>>15913632
>>15913635
wtf are you on about?

[Barkun No.15913642]

>>15913640
Fart in my mouf.

[Anonymous No.15913643]

>>15913630
Limits are easy to define. Given a potentially infinite sum, at any point in the sum, the sum will be less than the limit.

[Anonymous No.15913651]

>>15913643
1) series are a special case of a limit, define the correct thing please
2) not even close to a formal definition, again infinitists can do this task trivially
3) congratulations on making a definition that proves that the sum from n=1 to inf of (1/2)^n is 50

[Anonymous No.15913655]

>>15913651
1) same for sum but with series
2) who cares
3) the limit is the smallest value with such a property

*yawns*

[Anonymous No.15913664]

>>15913655
1) what?
2) any actual mathematician who wants to prove theorems instead of schizo garbage does
3) are you telling me you believe in numbers with some sort of "least upper bound" property? Please define precisely these numbers you are working with. If defining the whole set at once is offensive to you, feel free to define an arbitrary element instead

[Anonymous No.15913666]

If you clowns are my competition, this thread gives me hope I can solve the Continuum Hypothesis first and have the envy of Godel's ghost. I don't there's any stupid meme prizes for solving CH, all the better.

[Anonymous No.15913668]

>>15913664
I’ve already established that the naturals can be defined while also being treated as a potentially infinite set. Again, finitists can do the same mathematics and get the same real-world results, but without the unnecessary Cantorian nonsense

[Anonymous No.15913672]

>>15913666
there is no continuum hypothesis, retard. Different sizes of infinity is a contradiction. And that’s why no one will ever “solve” it. It makes no difference either way. Such math is absolutely useless in the real world

[Barkun No.15913673]

Will I be banned for what I done today?

I CANT HELP IT IM SICK

[Anonymous No.15913676]

>>15913668
The naturals are not enough as they do not permit talking about fractions which I assume you want to do. To resolve my (1/2)^n example a couple posts ago, you alluded to numbers are or at least contain the rationals and which satisfy some sort of least upper bound property. That is what I am asking you to define.

[Anonymous No.15913683]

>>15913676
The reals have the least upper bound property. But like the naturals they are still potentially infinite.

[Anonymous No.15913696]

>>15913683
Yes, I know the name of the set I'm referring to. I'm asking you to define this set or an arbitrary element of it in a way compatible with finitism.

[Barkun No.15913707]

>>15913696
You've set me up with a normal oriented message on Starfield when it is aligned automatically to the alternative reality I have. The sweet spot is found going left for a short period and then you change to the external.

[Barkun No.15913709]

>>15913696
And all your messages are fog at best.

[Anonymous No.15913713]

>>15913707
>>15913709
take your meds

[Barkun No.15913716]

>>15913713
The chaos after war if I shut up now will be brilliant for you. You'll profit immensely if my act today is treated properly. Hopefully the jannie forgives me. I am experiencing a nervous attack. I think everyone's plotting against me and I'm warring at times. Oh well. See ya.

[Anonymous No.15913721]

>>15913672
>Such math is absolutely useless in the real world
Most math is useless in the "real world". Guess you are more interested in calculating the flow of jism into your ass with the boring old Navier Stokes and it's stupid prize money. There are different sizes of infinity as per Cantor and Godel thought CH was interesting and I trust G's opinion more than yours.

[Anonymous No.15914235]

>>15913643
At the first point of the sum 1-1+0+0+0+... the sum is 1 which is less than the limit.

[Anonymous No.15914267]

>>15912121
>The members of the set of fractional numbers between 1 and 2 simultaneously add up to 1 (since they're the amount 1 and 2 are separated by)
Wtf are you talking about? You seem to be conflating summation with some weird notion of measure.

[Anonymous No.15915106]

>>15913614
A limit it just the study of
>This gets closer to that
There's no need to make vast metaphysical assumptions about reality for such a thing

[Anonymous No.15916158]

>>15913721
>There are different sizes of infinity as per Cantor
This is itself a contradictory notion. Tell me two infinities of different sizes and I'll prove they both are and are not the same size.

[Anonymous No.15916164]

>>15916158
Okay, I'll feed the troll: explain to me how the naturals has the same cardinality as the reals.

[Anonymous No.15916170]

>>15916158
Are all circles the same circle but just different magnitudes

[Anonymous No.15916286]

>>15916164
Say in an Infinitist world you were about to have a showdown between two kings

Whichever has the largest army is guaranteed to win the battle. If they have the same size it's a tie.

King Naturalus has his army composed of soldiers with numbers on their badges corresponding to the natural numbers (Pvt. 1, Sgt. 2, Cpl. 3, and so on)

King Realus has his army composed of soldiers with numbers on their badges corresponding to the real numbers.

King Realus has more and will win.

But King Naturalus has a plan: without adding any soldiers to his army, he has them erase their name badges and relabels his line with the real numbers instead.

Does King Realus still win the battle?

[Anonymous No.15916323]

>>15916286
yeah, changing a badge does not change the soldiers that have the badge, in the same way that changing the badge's content to "fox" won't make the soldier a member of the species vulpes vulpes, you analogy doesn't suck ass, it straight up blows air in the ass, like a retard that misunderstood what the fuck a blowjob is, jesus christ
fucking hell, given that Natutardletsky's the XXVIIth army was in one to one correspondence with the naturals we can then take the fucking army and make a list of the real numbers the soldiers changed their badge name to, the order in which we note them is utterly meaningless, then we can do the diagonal argument and show that there is a real number in Real of a Down's syndrome's army which ain't on Natutardletsky, and as a matter of fact, there are uncountably many more, so yeah, Natutardletsky looses, and you are an embarrassment to your parents, do not show them you failed analogy, they have already endured enough of your fucking failure, my god... if you have studied philosophy, you are a god damned double failure of a man.

[Anonymous No.15916335]

>>15916323
...That's about the quality of response I expected.

>then we can do the diagonal argument and show that there is a real number in Real of a Down's syndrome's army which ain't on Natutardletsky
Which Real number wouldn't be present?

[Anonymous No.15916363]

>>15916335
the one that don't mach the fucking one in the natural king's army you sub-baboon, oh and don't think for a moment i'll let you get away with a meager remark of what you think to be the value and or quality of my response to your probable festering corpse-tier analogy with out fucking addressing my responses content, you whole grain retard
what fucking number, irrelevant, no matter the list a number can and will be constructed that is not on the fucking list, I already fucking said on my response to your abortion of an analogy THAT THE ORDER OF THE LIST IS UTTERLY IRRELEVANT, YOU ELECTROENCEPHALOGRAPHIC FLATWORM

[Anonymous No.15916823]

>>15916335
its the only quality you should expect displaying such a dumb misunderstanding of the notion you are trying to contradict.

[Anonymous No.15916839]

>71 posts
>25 IPs
just one sad samefag self bumping it's lame vanity thread over and over again

[Anonymous No.15916940]

>>15916363
>the one that don't mach the fucking one in the natural king's army
Which one is that, again?

>no matter the list a number can and will be constructed that is not on the fucking list
You're welcome to do so; the battle starts soon and this is vital intelligence.

[Anonymous No.15917136]

>>15912121
>the infinite addition of positive numbers greater than zero equals infinity
Literally false.

[Anonymous No.15917329]

>>15917136
If a number is positive and nonzero then by definition its addition advances some quantity along the number line. Advance along the number line infinitely and your value is ∞.
Except this also can't be true because the distance between 1 and 2 is an infinite number of infinitesimals. But it has to be true. But it can't be true. But it has to be true. But...

Actual infinities simply always lead to contradictions.

[Anonymous No.15917741]

>>15915106
>This gets closer to that
You sound suspiciously like someone who learned the correct intuition in high school but cannot formally explain what they are talking about.
>vast metaphysical assumptions
I find it to be a weak and highly intuitive metaphysical assumption. Draw a line and express that line as a set of points. How many points are in the set?
>>15916286
>asked to prove simple mathematical claim
>responds with brain-dead analogy
The analogy doesn't even work. The relabeling process is impossible, which of course is the definition of one set having a larger cardinality than another.

[Anonymous No.15918148]

>>15917741
Based line contemplater

[Anonymous No.15918357]

Prime tetration foundation

[Anonymous No.15919416]

>>15917741
>but cannot formally explain what they are talking about
There's a problem with getting too lost in the concrete world that you can't work in the abstract (like early objections to negative numbers), but the opposite can be true where you get too into the abstraction and lose sight of the concrete picture. A limit, boiling it down, is just a model of this getting closer to that.

>I find it to be a weak and highly intuitive metaphysical assumption. Draw a line and express that line as a set of points. How many points are in the set?
By metaphysical assumptions, I was referring to really believing actual infinities exist in the physical world because of limits in math.
If you've drawn a line with a pencil then it has as many points as it has graphite molecules and no more. You can use the line to represent a fictional infinitely divisible object, but it's simply a useful fiction. A series of graphite or ink molecules is no more a line segment in the mathematical sense than a plastic Enterprise toy is a starship.

[Anonymous No.15919421]

>>15917741
>The relabeling process is impossible
Why?

[Anonymous No.15919500]

>>15919416
I'm not asking you to get lost in abstraction. I'm asking you to provide a precise definition of what you're talking about, which is a trivial task for a real mathematician. It doesn't have to be in a formal language, English will do as long as it's mathematically precise.
>drawn a line with a pencil
OK, I was speaking very slightly metaphorically when I said "draw a line". I guess it should be expected that a thread like this would take things excessively literally. What I meant was to consider a line as a completed geometric object in Euclidean space, then consider the set of points in that line. Depending on your definitions, this set is either identical to the line or simply uniquely corresponds to it; either way, the fact that I can consider a line in this way is an obvious intuitive truth.

>>15919421
>Why?
By asking for a relabeling process that changes each natural number to a real number without missing any, you are asking for a surjection from N to R. But this is not possible (try using Google, there are several proofs of this fact).