/sci/ - Science & Math

[Anonymous No.10768070]

[math] - \infty [/math] is the greatest number, because [math] - \infty +1 = - \infty [/math]

[math] + \infty [/math] is also the greatest number, because [math] + \infty +1 = + \infty [/math]

therefore [math] - \infty = + \infty [/math].
For this reason the usual order relation on the reals/rationals/integers cannot be consistent, and therefore cannot exist.
Infinite sets are a scam, and putting your fingers in your ears while shouting won't make our understanding of mathematics any better.

[Anonymous No.10768078]

>>10768070
low iq post.

[Anonymous No.10768080]

>>10768078
>putting your fingers in your ears while shouting won't make our understanding of mathematics any better.

[Anonymous No.10768137]

>>10768070
>therefore -inf is inf
you can't tell your ass from your elbow

[Anonymous No.10768243]

>>10768137
I couldn't if I was an """infinite""" set.

[Anonymous No.10768244]

>>10768070
Infinity isn't real and cannot be traited like you did

[Anonymous No.10768252]

>>10768243
The mathematics of infinity stretches back to ancient Greece and India.

applying bounded logic to something which is by definition boundless is not only futile, but outright retarded.

Also, |-inf| = |inf| for the naturals.

This is by definition correct you fucking mongoloid.

[Anonymous No.10768308]

>>10768244
I treat it that way, what are you going to do about it?

[Anonymous No.10768311]

>>10768244
>traited
fucking traitors

[Anonymous No.10768315]

>>10768252
>Greece and India
so pedo = poo and it's all natural

[Anonymous No.10768364]

Alright I'm a brainlet compared to the people who actually understand math here so save your insults
My question is if we use [math]\infty[/math] as the last number, and tend to insist that it's the last possible number while also adding to it while still insisting that there's nothing greater than it even including this addition itself, shouldn't it then result into an overflow of [math]\infty + x = -\infty + (x - 1)[/math] as if you've wrapped around and entered into the negatives? If not, why isn't such a thing possible?

[Anonymous No.10768395]

>>10768070
>he thinks infinity is a number.
Low quality bait

[Anonymous No.10768413]

>>10768364
>if we use ∞ as the last number
we don't, it isn't even a number

[Anonymous No.10768415]

>>10768364
>, why isn't such a thing possible?
why aren't opposite ends of a stick next to each other?

[Anonymous No.10768431]

>>10768364
The topologies of [math] \mathbb{R}[/math] and of [math] S^1=\mathbb{R}+\{\infty\} [/math] are different.

[Anonymous No.10768444]

>>10768413
then what is it

>>10768415
because the stick doesn't extend to infinity in both sides, which in a closed system like our Universe that is limited by the radius of inflation, is not possible as both ends would eventually meet if they were truly infinite - i.e approaching the limit of that radius and bending around the sphere as energy cannot "exit" the Universe?
In such a case isn't infinity just a placeholder for the maximum length of the radius of such a closed system, because we do not know what the exact value is so therefor we use a symbol? Because if it's just an open system that expands infinitely in both sides, then that not only doesn't apply to our reality but it's also retarded and useless. The fact that there can be absolutely no potential use of an infinitely-expanding infinity within our Universe means that any definition other than it being the last number of the set is absolutely useless

>>10768431
so what happens if we just do this https://en.wikipedia.org/wiki/Extended_real_number_line

[Anonymous No.10768457]

>>10768444
>then what is it
An unbounded quantity that is greater than every real number.

>because the stick doesn't extend
it's just a metaphor ffs

[Anonymous No.10768681]

[math]-\infty < 0[/math]

[math] \therefore [/math] you're retarded

[math]\square[/math]

[Anonymous No.10768707]

Of course, neither the natural numbers, the integers, the rationals, nor the real numbers are defined to include [math] /infty [/math] or [math] -/infty [/math].
If OP wants to extend one of these sets to include an infinity, he has to answer::
(1) How to extend the topology: what are the open sets and the closed sets now?
(2) How to extend the order relation: how do we compare an infinity with another element?

(3) How to extend arithmetic: what are sums, differences, products, and divisions involving infinity?

(4) Why are we doing this anyway?


Some sets of possible answers to these questions are actually useful, but you shouldn't expect without proof that any particular property of the real numbers will apply to the real numbers extended in some way by one or two infinities. In the OP, neither of the two equations given as reasons actually imply anything about ordering absent further definitions. (But I doubt OP's sincerity.)

[Anonymous No.10768724]

>>10768070
>implying there is only one unique greatest element

[Anonymous No.10768791]

>>10768444
It's a symbol reserved for situations when we want to describe a quantity growing without bounds. It is not a fixed "place" on the real line, it's more like a constant growth in a certain direction and at a certain speed.
This is basic. Study calculus.

[Anonymous No.10768803]

>>10768791
>a quantity growing
n ---> inf
sorry anon, you're talking about the n
not the inf

[Anonymous No.10768957]

>>10768070
so you're defining the greatest number as the number such that if you add 1 it remains the same number? and you're postulating that there is only one greatest number?
If you want to make a meaningful proof you have to make everything explicit. Usually there is only one greatest number because things are linearly ordered

[Anonymous No.10769003]

>>10768803
Read again. In the situation you described, n -> inf literally translates to "n grows without bounds". Infinity is not a number in this situation, nor is it ever intended to be. Trying to discuss it as a number is foolish. The only time when we "add" something to infinity is when doing limit algebra, which does not deal with numbers, but with limits. Again, basic tenets of calculus.

[Anonymous No.10769044]

>>10769003
you are claiming n is inf
protip: it isn't

[Anonymous No.10769048]

Maybe the real infinity were the friends we made along the way?

[Anonymous No.10769053]

>>10769003
>n -> inf literally translates to "n grows without bounds"
not that guy but it really doesn't. It means that n approaches the end of the reals because the result of the limits is always a constant value, implying that the value that n has approached is also constant and not a boundless growth in a direction else limits like [math]\lim_{n\to\infty} \frac{1}{n}[/math] would never truly reach 0 under a boundless continuation
math doesn't have a temporal progression so it's stupid to assign one to it like infinite growth as that is a temporally infinite function which will never result in a concrete value within the framework of a single execution, i.e writing a finite equation and going through it once to reach the same value as if you'd go through it millions of times
As long as we're working with temporally-finite equations, temporal infinity is physically impossible to exist, so therefor "increases forever" does not exist.

[Anonymous No.10769054]

>>10769048
does your infinity owe you $20 too?

[Anonymous No.10769073]

>>10769053
>the end of the reals
no such thing

[Anonymous No.10769082]

>>10769073
>NOOOO they just extend forever in temporal infinity nevermind that the concept used to signify that extension always results into constant values which doesn't at all imply that it is a static constant value as well

[Anonymous No.10769185]

>>10769053
You have no idea what a limit is, do you? Graph y=f(x)=1/n. Does the value in the y axis ever reach 0? Spoiler: it doesn't. As x grows without bound, y gets closer to 0 but never reaches it. 0 is a bound or limit, we know for sure that y never reaches it. It is not "the end" of the function, it is not the "end" of the reals because there is no such thing defined and it would be useless to do so. But hey, if you want to do it go ahead, let's see how much better your mathematics works, maybe we'll learn a thing or two. I really doubt it, though, but you'll probably realize what you're not wanting to see.
Also that whole temporally-finite equation nonsense is really embarassing man. There are endless functions that never stop moving as x grows indefinitely. We care about their limits because we want to know their shape. Study basic series problems and you'll see how an infinite (yes, infinite as in endless) sum can be algebraically manipulated to show that it equals a concrete value. Hell, I'll say the same thing again: actually study calculus, instead of coming here and trying to sound smart while evidently lacking knowledge of the basics.

[Anonymous No.10769192]

>>10769082
>temporal infinity
imagine being this much of a math brainlet in {{current year}}

[Anonymous No.10769224]

>>10769044
Sigh. Whatever, man. Hope you guys actually pick up a calculus book or couse at some point instead of trying to larp as revolutionary topminds in an imageboard.

[Anonymous No.10769259]

>>10769185
>Graph y=f(x)=1/n. Does the value in the y axis ever reach 0?
Precisely. When you try to graph it, you proceed to draw a time series data of its historical values which is physically impossible to be achieved because what you're attempting to do that way is to create a truly-infinite function - one that executes infinitely through time and has infinite steps which you denote by the points on the graph. This is useless to us because not only is it not achievable within this Universe, it's also not applicable to anything. What is both achievable and applicable, however, is pretending that this process eventually terminates somewhere, which is the last member of the set, but since we have no information on what its precise value or location is, we use infinity to denote it, allowing us to reach it with a single execution without having to calculate and graph the infinite steps towards it, i.e, it's temporally finite in the exact same way that a finite limit that approaches a finite number is.

>Study basic series problems and you'll see how an infinite (yes, infinite as in endless) sum can be algebraically manipulated to show that it equals a concrete value.
You mean the analytic continuation of divergent series that are absolutely useless to us, which then forces them to converge by converting them to temporally-finite useful series, i.e exactly what I'm talking about?

>>10769192
That's the shortest way to describe the infinite execution of the same function without it converging to something constant. Because if I just say infinity people will keep talking about infinite growth and completely miss the point of what I'm trying to imply, so I'm trying to accent the fact that you need infinite time to complete these functions which is different from infinite length, which is physically limited within our Universe to a constant value.

[Anonymous No.10769288]

>>10769224
the difference in real
[math]
\lim_{n \to \infty}1^n = 1 \\
1^\infty = \text{undefined}
[/math]

[Anonymous No.10769295]

>>10769224
there is a real difference
[math] \displaystyle
\lim_{n \to \infty}1^n = 1 \\
1^\infty = \text{undefined}
[/math]

[Anonymous No.10769307]

>>10769259
>You mean the analytic continuation of divergent series that are absolutely useless to us
>geometric series with |r|<1
>divergent
>useless
gr8 b8 m8 8/8

[Anonymous No.10769324]

>>10769295
yes, and it's not the one you think.
protip: the latter case are not numbers per se, but limits. that's why they don't appear beside the limit operator, like the number and variable in the form case. learn the difference.

[Anonymous No.10769327]

>>10769224
>took a calc course and now thinks he's a genius

[Anonymous No.10769333]

>>10769324
n =/= inf
that's why the results are different

[Anonymous No.10769484]

>>10768070
Yes, on the Riemann sphere all lines converge to the same infinity.

[Anonymous No.10769497]

Infinity is a amount of numbers. If you want to use a infinetly big number, you have to use another greek letter which i dont remember right now. Also every single thing you did is wrong