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/sci/ - Science & Math

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11283611 No.11283611 [Reply] [Original]

Infinity equals the number of points from 0 to 1. No more, no less

>> No.11283615

>>11283611
>no less
uhhhh

>> No.11283617

>>11283611
The infinity from 0 to 1 is a larger infinity than counting the integers from 1 to infinity.

>> No.11283625

>>11283617
No it isn't, just map each number from 0 to 1 to a corresponding whole number without the decimal.

>> No.11283639

>>11283625
>just map each number from 0 to 1 to a corresponding whole number without the decimal.
lmao easier said than done. Do we begin at .00001 or .000001?

>> No.11283643

>>11283639
We begin at zero. You count up with each infinitesimal. .0001 coresponds to infinity/10000.

>> No.11283647

>>11283643
Sorry when I say 0 to 1 I mean an open set with the boundaries 0 and 1.

>> No.11283650

>>11283643
How is infinity/10000 a whole number thought

>> No.11283651

>>11283647
The set is half closed, including 0.

>> No.11283654

>>11283650
Just use a base in which it would result in a whole number

>> No.11283671

>>11283643
You are basically turning x c ]0,1] into 1/x

But since a lot of numbers y = 1/x arent integers youre just wrong

>> No.11283679

Infinity does not, in the strictest sense, equal anything, not even itself. This is of course because infinity is a concept and not a number. When we say that 1+2+3+4... (By partial sums, not Cesaro or Ramanujan) equals infinity, what we really mean is that "this explodes to a very large number we can't keep track of." For instance.

>> No.11283686

>>11283671
No I'm translating x into infinity times x. Everything becomes a whole number, including infinitesimals

>> No.11283689

>>11283686
Infinity times x equals infinity

>> No.11283692

>>11283689
Wrong. That doesn't hold for infinitesimals, sorry

>> No.11283693
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11283693

>>11283611
>implying real numbers exist
(They dont)

>> No.11283696

>>11283692
Who cares about infinitesimals, you said that the number of points between 0 and 1 equals infinity, not less

>> No.11283701

>>11283696
Just showing that x*infinity doesn't equal infinity

>> No.11283710

>>11283679
Stop shitting on Cantor’s work brainlet. Infinity is a number with size/s.

>> No.11283742

>>11283679
>this explodes to a very large number we can't keep track of.
This is false though, there is no final real number.

>>11283617
This is false, they are both exactly the same size, Aleph naught.

>> No.11283779

>>11283611
Infinity is just an 8 that fell over

>> No.11283792

>>11283617
based

>> No.11283803
File: 22 KB, 415x274, that sci feel.png [View same] [iqdb] [saucenao] [google]
11283803

OMG INFINITY!!!!
THE BIGGEST NUMBER!!!
EXTREME SCIENCE!!!

>> No.11283813

>>11283611
This is wrong in so many ways. First off, the number of real numbers (whether we are considering (0,1) or [0,1]) between 0 and 1 is only one type of infinity (it can actually be shown that there is a bijection between both of these intervals and the entire real number line). The cardinality of the natural numbers is a completely different type of infinity, which is actually smaller than the cardinality of the real numbers. the cardinality of the real numbers is equal to the cardinality of the power set of the natural numbers.

>> No.11283816

>>11283803
BILL BILL BILL BILL BILL BILL BILL BILL BILL BILL BILL BILL BILL BILL BILL!

>> No.11283841

>>11283813
>there is a one to one mapping between [0,1] and [0,infinity]
yeah right

>> No.11283849

>>11283611
what about the points from -1 to 0

>> No.11283855

>>11283841
One is infinitely large and one is infinitely small, how can anyone make a case for which is “infiniter”? This whole thread is stupid we all understand the concept of infinitely large and small numbers, and like this thread it’s gonna go on and on, ad infinitum ad nauseam.

>> No.11283858

>>11283855
It's easy to make a case because all of the points are used up mapping [0,1] to [0,1], bro

>> No.11283861

>>11283617
Its actually slightly smaller since .999...=1.

>> No.11283877

>>11283858
no they aren’t zoom in more

>> No.11283879

>>11283877
Then we can zoom in on the other [0,1] too

>> No.11283884

>>11283879
how far we zoomin’? x10? x1000? times... infinity?

>> No.11283888

>>11283884
Any amount bro

>> No.11283889

>>11283841
https://youtu.be/i7c2qz7sO0I?t=4m25s

>> No.11283890

>>11283841
First off, my original claim was that there exists a function f:(0,1) -> (-inf,inf), not [0,inf), but I can also give you an example of such a function.
Second, you used a closed bracket for infinity which just shows how much of a brainlet you are.
Third, define the function f:(0,1) -> (-inf,inf)
by the function f(x) = tan[pi*(x-(1/2))].
This function is a bijection between (0,1) and (-inf, inf).
Fourth, learn some set theory you fucking normie. I would suggest reading a book by Halmos.

>> No.11283896

>>11283888
We must approach closer to the zero... never touching it...
As long as it takes!
Godspeed fellow infinityplotting anon.

>> No.11283899

>>11283890
Typical brainlet. That's like saying 2x maps [0,1] to [0,2]. At the infinitesimal level, the function skips every other number.

>> No.11283905

>>11283899
The example you just gave IS a bijection between those two sets. Your example isn't a refutation of anything that I said.

>> No.11283910

>>11283905
It's not a bijection. Take an input of 0, the output is 0, an input of infinitesimal returns 2*infinitesimal. The function doesn't return any odd infinitesimals.

>> No.11283913

the concept of an infinitely large number of things and an infinitely small number of things are both irelephant!
: ===D haha fug

>> No.11283919

>>11283877
see
>>11283858
at what zoom can you map .999,,, to 1 and to the two corresponding values in the set from 1 to infinity and what are those values?

>> No.11283930

>>11283910
First off, it is a bijection. To show it is a bijection, we must show that the function is one to one and onto.
To show that it is one-to-one, we must show that f(x)=f(y) implies x=y. Clearly 2x=2y implies x=y.
To show that it is onto, suppose z is an element of [0,2]. Then clearly z/2 is an element of [0,1] and f(z/2)=z.
These two facts establish the bijection. Second, you're incorrectly treating infinitesimals as if they were nature numbers you autist.

>> No.11283941

>>11283930
It's not one to one mate, what number maps to 1 infinitesimal? Nothing, there is no half infinitesimal.

>> No.11283943

>>11283611
https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument

>> No.11283944

>>11283611
0 divides into 1 infinitely for negative fun.

>> No.11283945

>>11283943
That argument concerns the mapping of Z to R, not Z to [0,1]

>> No.11283946

>>11283941
the fact that you’re “going” to 0 from 1 has some major implications, as much as 1 to infinity does. YOU CAN’T JUST FUCK WITH ZERO LIKE THAT. BELIEVE YOU ME I’VE TRIED.

>> No.11283949

>>11283930
I was thinking of this proof, and to show the

> clearly z/2 is an element of

I couldn’t think of any way to prove it without using intermediate value theorem. Is there an easier way?

>> No.11283950

>>11283946
The number line is discrete at the infinitesimal level

>> No.11283952

Ni

>> No.11283954

>>11283861
>falling for the "some infinities are bigger infinities than other infinities" meme
Yes, and some zeroes are bigger than other zeroes. Oh wait that's wrong, by definition

>> No.11283956
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11283956

>>11283950
No.

>> No.11283960

>>11283956
I can make an argument but you'd have to use your brain. Using euclidean geometry, if you project 2x onto the x axis and onto the y axis, there are more points on the y axis than the x axis.

>> No.11283964
File: 21 KB, 270x187, B360C7BA-D768-4A89-A89F-ABD7D1D81391.jpg [View same] [iqdb] [saucenao] [google]
11283964

>>11283960

>> No.11283967

>>11283954
Okay, but 0 Fahrenheit is bigger than 0 Celsius.

>> No.11283969

>>11283950
>The number line is discrete at the infinitesimal level
Wrong. Such abstractions are boundless you fucking retard

>> No.11283970

>>11283949
Why not just use properties of inequalities?
0<=z<=2 implies 0<=z/2<=1 just by multiplying through by 1/2.

>> No.11283972

>>11283964
>Falling for the accredited source fallacy
That's just a bad appeal to authority

>> No.11283975

>>11283969
BE NICE
MAY YOUR PATIENCE AND KINDNESS BE BOUNDLESS
T. INFINITESIMAL INFINITYPLOT GANG

>> No.11283976

>>11283969
I think you mean baseless, top kek

>> No.11283978

>>11283967
Fair point, zeroes are ghey

>> No.11283979

>>11283976
Did I stutter, retard?

>> No.11283981

>>11283625
It's proven that you cant. And the proof is really easy

>> No.11283983
File: 40 KB, 647x659, 6BC10E76-184C-4AAA-9BD6-D66CCED21503.jpg [View same] [iqdb] [saucenao] [google]
11283983

>>11283972

>> No.11283984

>>11283981
I've seen the proof, and I don't think it's valid

>> No.11284012

>>11283970
Whoops thanks

>> No.11284014

>>11284012
The issue is that you have to show a unique mapping. Since there are twice as many points from 0 to 2, each point maps to two other points and it isn't unique.

>> No.11284025

>>11284014
Then it doesn't map to two other separate points, it maps to a single unique range of points with double the magnitude of the original point range.

>> No.11284028

>>11284025
Then it isn't a bijection. In a bijection, each point has to uniquely map to only one other point, It doesn't map to a range.

>> No.11284038

>>11284028
No, it has to map to one mathematical element and in this case, that element is a range.

>> No.11284046

>>11284038
The argument is about how many points there are, not how many ranges there are.

>> No.11284050

And if each point maps to a range of points then that shows that one set is bigger than the other.

>> No.11284052

>>11284046
around 69
>>11284050
Not unless you can show that one set terminates first because if they are both unbounded they are ultimately no different in size.

>> No.11284053

>>11283611
Nothing equals infinity, since it's not a number.
You can say something "tends towards infinity", but you can't say it "equals infinity".

>> No.11284055

>>11284052
One set obviously terminates first. [0,1] maps onto [0,1] and there are no more points to map onto [1,2]. Don't act up your shenanigans

>> No.11284059

>>11283625
You are falsely assuming the decimal expansion has to terminate at some point.
It depends on if you look at the real numbers between 0 and 1, or the rational numbers between 0 and 1, which kind of infinity you are dealing with.
For former one is larger than the set of the natural numbers.

>> No.11284061

>>11284059
No, because the integers go on infinitely. You don't have to assume the decimal ever stops.

>> No.11284064

>>11284055
>no more points
There are infinite points when that set is broken down into infinitesimals, so no matter how many finite points you remove, you will still have infinite points remaining, so saying you will have no more points is a nonsense statement.

>> No.11284065

>>11284061
>You don't have to assume the decimal ever stops.
You have to, since otherwise you can't represent it as an integer.
Every integer has a finite length.

>> No.11284069

>>11284064
You're saying that if you remove some points you have the same number of points. That's nonsense, it's a smaller infinity. Per my OP, it's less than infinity.

>> No.11284072 [DELETED] 

AAAAAAAAAAAAAAAAAAAAAAA

>> No.11284075

>>11283611
Cantor showed if you try to map points from 0 to 1 to decimals, there will always be unmapped numbers remaining no matter how you order them. He did this with the diagonalization argument. Therefore, aleph 1 is greater than aleph nought.

>> No.11284076

>>11284065
Only 1 has to be represented with an infinite length integer. 1 maps to infinity. Every other decimal maps to a finite integer.

>> No.11284083

>>11284075
Nonsense. Here's another way you can map all of them. 1 maps to 1, 2 maps to 0.5, 3 maps to 0.25, 4 maps to 0.75, and on. Eventually you will map all of the numbers, by splitting each of the intervals in half with each integer.

>> No.11284087

>>11284069
No, I never said infinity was a number, it is a limit or a condition and no matter how many points you remove, you will have the same unbounded upper limit of points remaining and the condition where you have infinite points to draw from will remain in tact.

>> No.11284091

>>11284087
Yes, but for any given point p, per your argument, you've shown that it must be used up twice because it has to map onto a range. Therefore the number of points shrinks as you use them.

>> No.11284095

>>11284075
There will always be numbers ready to be mapped onto those remaining numbers too, though, because eventually you will reach the superposition of .999 which also equals 1 and every point will just be able to map onto either of those points which happen to be the same point.

>> No.11284102

>>11284091
>the number of points shrinks as you use them.
No because the infinity limit is a relativistic condition that scales evenly to all frames of reference, so it never actually shrinks or grows because an unbounded scale is always just a uniform straight line that never converges to an actual positive or negative value or terminates to a null value.

>> No.11284110

>>11284102
That's basically the reasoning that leads to the banach tarski paradox. You don't have the same number of points after you remove some. Infinity minus 1 is less than infinity. Sorry.

>> No.11284112

>>11283679
>This is of course because infinity is a concept and not a number.
1 is a concept. 3 is a concept. please define “number” as precisely as possible.

>> No.11284125

>>11284112
a number is an exact quantity

>>11284110
Again... infinity is not a number, its an unbounded limit, but if you remove 1 point from and unbounded set of points, you still have an unbounded number of points which can be removed from the set and no less.

>> No.11284129

>>11284125
So you also think by rotating spheres you can create more spheres from nothing, Kek

>> No.11284138

Anyway, if my thread is correct then infinity only equals the number of points from 0 to 1, and if you remove a point it's less than infinity. This is all just speculation.

>> No.11284145

>>11284129
Aren't you referencing a theorem that comes with a strong form proof?
Doesn't even the most basic Windows 95 screensaver that assumes the cross section of an infinite digital screen space demonstrate the proof of that theorem?

>> No.11284148

>>11284145
The theorem is incorrect because rotation doesn't create anything, mongoloid. That's why it's a paradox. Paradoxes aren't real.

>> No.11284152

>>11284148
That is not what paradox means, though.
Paradox just means a subversion of expectations that can actually be proven true even though it seems logically self defeating.

>> No.11284156

>>11284152
A paradox implies incorrect assumptions or incorrect reasoning. Sorry, but the paradox is the latter. You can't create something from nothing.

>> No.11284158

>>11284156
Good thing the theorem you are referencing creates something out of something plus rotations and translations, such that your statement doesn't even apply.

>> No.11284167

>>11284158
Good thing that you're dumb, such that you suck ass

>> No.11284173

>>11284167
Good thing you always have to argue about stupid shit, such that nobody loves you and nobody ever will.

>> No.11284174

>>11283816
????

>> No.11284175

>>11284076
I think you don't understand what I mean.
Take for example Pi, the Euler number, Sqrt(2).
The decimal expansions of these three numbers are infinitely long, and there is no simple pattern in them.
Essentially you get "random" digits all the way, and that way never ends, so these numbers can't all be mapped to unique integers.
There are a lot more numbers like these than there are numbers that have a finite decimal expansion.
Countably infinite vs. uncountably infinite
Look it up yourself. It's first year college stuff.

>> No.11284512

>>11283710
Exactly part of my point- it is a concept of varying size depending on the particular infinity, meaning that it can't be said to equal itself.

>> No.11284513

>>11283742
Maybe I phrased it poorly. You're right.

>> No.11284514

>>11283625
>what are irrational numbers

>> No.11284565

>>11284514
Irrational numbers are like infinitesimals. If infinitesimals are mapped to small integers, then irrationals between 0 and 1 are mapped to nearly infinite integers like other large decimals.

>> No.11284568
File: 1.19 MB, 680x1772, 1491856719978.png [View same] [iqdb] [saucenao] [google]
11284568

>OP's in grade school

>> No.11284573

>>11283742
>This is false, they are both exactly the same size, Aleph naught.

No, subset of reals from 0 to 1 has the same cardinality as the entire reals

>> No.11284618

https://en.wikipedia.org/wiki/Subcountability

>> No.11284644

>>11283643
okay so first number is 0, what's the second number ??

>> No.11284647

>>11284573
The set of subsets of the interval from 0 to 1 actually has a strictly larger cardinality than the set of reals.

>> No.11284655

>>11284647
I set subset of reals not set of all subsets, which is just the power set and the next aleph number in terms of cardinality.

>> No.11284660

>>11284655
Okay then. But some subsets do have smaller cardinality, so either way.
Anyway, you can give up on OP. For some reason he seems to think that multiplying an infinitesimal by a real number can produce anything other than another infinitesimal.

>> No.11285052

>>11284644
Infinitesimal, smartass

>> No.11285473
File: 13 KB, 1069x83, infmul.png [View same] [iqdb] [saucenao] [google]
11285473

>>11283701

>> No.11285511

>>11283611
No it equals the number of points between any two rational points.

>> No.11285542

>>11285473
The limit is [math]\infty \cdot c[/math], not [math]\infty[/math]

>> No.11285548

>>11283611
Does that include the complex numbers?

>> No.11285550

>>11285548
no

>> No.11285572

>>11284514
[math] \mathbb{P} [/math]

>> No.11285577
File: 1.14 MB, 1000x675, be40f1f9a015c1d61bc801ee7b0b5ab2.png [View same] [iqdb] [saucenao] [google]
11285577

>>11284655
>set of all subsets, which is just the power set and the next aleph number in terms of cardinality

swiftly adopting the Generalized Continuum Hypothesis, get this hothead outta here

>> No.11285595

>>11284053
The 'equal' sign is just an operation describing substitution. Assuming you have one transfinite set containing all even numbers, and another transfinite set containing all odd numbers, the two could be substituted for one another on a cardinal level. In a sense, we are substituting one infinity for another.

>> No.11285650 [DELETED] 

>>11285595
get this hott-head outta here

>> No.11285652
File: 1.04 MB, 1899x2500, NINTCHDBPICT000543123093.jpg [View same] [iqdb] [saucenao] [google]
11285652

>>11285595
>equality on sets is given by being isomorphic/in bijection

get this Hott-head outta here

>> No.11285665

>>11285542
For any real number (>0) that's the same.

>> No.11285672

>>11283679
>infinity is a concept and not a number
Based Zeno

>> No.11285757

>>11285052
so what's the number ?

>> No.11285928

>>11285757
an infinitesimal