Is infinity pseudo science?

depends entirely on your definition of Temperature. You could make a case for nearly anything here^^ If you take electron energy levels or boltzmann inversion here you could talk about a NEGATIVE temperature ( on the kelvin scale) which is actually hotter than say "1K" and depending on your (naive) definition of temperature may as well be hotter than the hottest possible temperature, i.e. "infinite" for some definitions of infinity

Eh. Infinity is an axiom of ZFC. So in a way it's an assumption. But it's an assumption that gives rise to a staggeringly enormous amount of interesting mathematics. It also doesn't lead to any logical contradictions. So there's no problem in taking it as an axiom.

You're welcome to do math without the axiom of infinity but it just won't be as interesting. Nor will it be as useful.

Also if results like 0.999...=1 and 1/2+1/4+1/8+1/16+...=2 are not intuitive to you then you may actually be a retard.

Sorry, I meant 1/2+1/4+1/8+...=1 (not 2).

Why the apeirophobia?

people like you are the reason I took a 7 month hiatus from this board.

fuck off back to

Infinity has different meanings, all of which are very well defined in mathematics. Real numbers are (often) constructed as the equivalence classes of rational cauchy sequences whose difference converges to 0.

Science is literally empiricism. Math is not. Math is used in science to formulate hypotheses, but math itself is not an empirical investigation.

top 10 worst threads 2018

>top 10 worst threads 2018
Meanwhile the catalog is filled with IQ, racebait and /pol/ threads

Does one even exist? Like count apples. One apple, two apple. No you can't because an apple is an arbitrary measurement. Each apple has different and made of particles. There isn't one apple.

On a human scale, quantity makes sense. What would you suggest as an alternative?

>apples don't exist
the lengths to which you people will go

Infinity is pseudo intelligence.

Its not math, its not science, it's not intelligent.
To do infinite summation is to say you never stop summing, which means you can never acquire a result, which means infinite summation is not useful. If you can acquire a result from it, then there was an end to the summation and thus not actually infinite, unless you redefine infinity from "never ending" to "a greatest, real number value", meaning "infinite" is just a counter-intuitively retarded name for an obviousy finite number. If you then say "no greatest real number exists", then infinity doesn't then exist, which also makes it useless.

Infinity is a paradox, and as a paradox it is not useful.

[math]0.\bar{9 \neq 1[/math] because there can only exist a never ending amount of 9's never approaching anything but more 9's. The result of an infinite sum isn't defineable because you never reach an end result. The amount of 9's in 0.999... cannot be infinite unless "infinite" is used in lieu of "an arbatrarily large real finite number". The result of an infinite sum cannot equate unless "infinite" is used in lieu of "an arbitrary large real finite number". Furthermore, replacing "infinite" with "an arbatrarily large real finite number" then provides for [math]\frac{1}{\infty}>0[/math], meaning for "an arbitrary amount of 9's in 0.999..." would necessitate the addition of [math]\frac{1}{\infty}[/math] to properly sum 1, and "an arbitrary amount of summation" in an infinite sum to finitely equate a real value, and even though none of these steps actually logically worth regardless of definition, it still doesn't provide for any sense to be made about which number infinity is supposed to be.

Only brainlets who have been programmed by math instructors via obedience believe infinity is rigourosly defined or useful. It isn't.

>To do infinite summation is to say you never stop summing, which means you can never acquire a result
You're retarded. No one is sitting down to add each step in a summation algorithm, instead an analytical trick is used to transform that algorithm into something else that can be evaluated in finite steps.

>If you can acquire a result from it, then there was an end to the summation and thus not actually infinite
A finite amount can be divided into infinite parts, and therefore infinite parts can form a finite summation.

You have less understanding of the concept you are trying to criticize than an elementary school student, and treating you lack of basic understanding as a paradox. Dunning Kruger effect in action.

Saying there are an infinite, non-finite amount of parts between finite 1 and finite 2 means you can never reach 2 from 1 by incrementing in those parts.

Really you just projected by invoking dunning krueger when you had no idea what you were talking about but decided to post anyway. Moreover, you're selfish and evil for wasting my and anyone elses time in reading your completely uninformative post. You ultimately didn't even comprehend my post that you replied to and didn't understand the strict definitions offered.

[math]\sum_{n=1}^{\infty} \frac{1}{2^n}[/math] will never equal 1 or approach 1. It wont even technically equal 0.999...

The moment you have a sufficient amount of sequential 9's in the result to be assumed as infinite, you would also have an infinite amount of unordered random numbers after it. Cutting this entire value in half spacially, the left half from middle to the decimal point would be all 9's, but the right half would be random gobbledygook numbers in no defineable pattern, and that is already when more than all possible digits of the significand have been accounted for and filled, from the 1st decimal place at 0.9, to the infinite'th decimal place. For 1/2^n to properly approach 0.999... would require the total amount of digits be infinite, and only half of all those digits would be 9's so to cut off the latter half and assume 1/2^n = 0.999... is to actually say [math]\sum_{n=1}^{2 × \infty} \frac{1}{2^n}[/math] where after doubling on the infinite amount of summable iterations, there would finally be an infinite amount of 9's, even though it's still further followed by an infinite amount of arbitrary unordered digits of random numbers.

1/2^n is obviusly less than 2/3^n or 3/4^n, and these are all leas than 9/10^n which would be a true uninterrupted string of 9's.

Infinity isnt well defined or useful. Only brainlets pretend it is.

>your example : you use "=" in a completely other sense than you'd do in "x = 1",
Wrong.

>[math]\sum_{n=1}^\infty \frac{1}{2^n}[/math] will never approach 1.

Let's tackle this part of your claim. Note that
[eqn]\sum_{n=1}^k \frac{1}{2^n} = \frac{2^k - 1}{2^k}.[/eqn] We can easily see that this equality holds true for [math]k=1[/math]. Let [math]k\in\mathbb N_0[/math] be arbitrary and assume the equality holds. We show that it also holds for [math]k + 1[/math].
[eqn]\sum_{n=1}^{k+1} \frac{1}{2^n} = \sum_{n=1}^k \frac{1}{2^n} + \frac{1}{2^{k+1}} = \frac{2}{2}\cdot\frac{2^k - 1}{2^k} + \frac{1}{2^{k+1}} = \frac{2^{k+1}-1}{2^{k+1}}.[/eqn]
This proves that the equality holds for any arbitrary natural number greater than or equal to 1 and all that is left to do is show that [math]\frac{2^k - 1}{2^k}[/math] approaches 1.

Let [math]\varepsilon > 0[/math] be arbitrary. By the Archimedian property there exists some [math]k_0 \in \mathbb N_0[/math] such that [math]k_0 > \frac{1}{\varepsilon}[/math]. Let [math]k \in \mathbb N_0[/math] be arbitrary and assume that [math]k \geqslant k_0[/math]. It then follows that [math]2^k > k \geqslant k_0 > \frac{1}{\varepsilon}[/math]. From here it follows that
[eqn]\varepsilon > \frac{1}{2^k} = \left|\frac{-1}{2^k}\right|
= \left|\frac{2^k -1 - 2^k}{2^k}\right|
= \left|\frac{2^k -1}{2^k} - \frac{2^k}{2^k}\right|
= \left|\frac{2^k -1}{2^k} - 1\right|
[/eqn]

This proves that for any arbitrary distance [math]\varepsilon[/math] there is some point after which all the partial sums of the series lie closer than that and as such this proves that the series does approach 1.

this was meant to give you a (you) but you deleted the initial post so here is your (you).

While this is nice, it's rather misguided. In fact, the whole idea that an infinite sum ``approaches'' a number is wrong. An infinite sum is a complete object. It IS a number (assuming convergence). A convergent infinite sum is simply a different way of representing a number. So $\sum_{n=1}^{\infty} \frac{1}{2^n}$ is just a weird way of writing the number 1. Just like 2/2 is another way of writing the number 1.

It's kinda like having a nickname for somebody. You might refer to a friend as `Robert' while I call him 'Bobby'. We're referring to the same person, but in different ways. Same thing with the number 1 and that infinite sum. Different ways of referring to the exact same mathematical object.

If an infinitely large arbitrary number can exist, an infinitely small arnitrary number must then also exist.

If you use these definitions, the opposite of infinity is a value that is the closest to zero but greater than zero. If 0.999... = 1, then 1/infinity = 0.
If 1/infinity = 0, a/b = c
Then 1/0 = infinity, a/c = b.
If 1/infinity = 0, there does not exist an infinitely small real number, and therefore does not exist an infinitely large real number, thus infinity does not exist and neither does an infinite amount, thus this conversation is no longer about "0.999... & 1", because there is no rational, consistent, reliable way of defining what "0.999..." is without invoking infinity which itself is not rationally, consistently, reliably defined. If the concept of infinity cant work, you cant then take a next step by using infinity in any specific manner. Doing so is the equivalent of knowing infinity is unachieably countable but treating infinity+1 as real, as it's next step countable step. Non-finitests don't do this, so non-finitests are stuck forced to abritrarily force finitest rules on infinity without changing the definition of infinity. Infinity+1 doesnt rationalize as the next step after infinity, so using infinity doesn't rationalize as the next step after not defining infinity.

Infinity is a fucking paradox for brainlets. Just stop. Any and every attempt to justify using it is easily proven fallible, so anyone who tries to do it anyway is an idiot.

There is no such thing as getting a result from unending work. There is also no such thing as a largest real number. Infinity = worthless.

Oh I don't disagree, but he was just going to throw retarded retorts that "convergence isn't equality" so I just opted to show that the partial sums definitely do approach 1, which he also denied. And as you said, the entire series is indeed equal to 1.

>If an infinitely large arbitrary number can exist, an infinitely small arnitrary number must then also exist.
It can't exist and nowhere is it claimed to exist in the post you are replying to.

>It can't exist and nowhere is it claimed to exist in the post you are replying to.
Yes, infinity can't exist, thanks for agreeing.

I bet you didn't even realize thats what you typed. I think its time to take a step back and realize this thing called infinity is fully retarded, and trying to justify it just leads to people becoming retarded.

There are no real numbers that are "infinitely large", the same is true for natural numbers. That claim is in no way equivalent to "Infinity can't exist". There is no upper bound to the natural numbers or to the real numbers, which is what we mean when we say there are "infinitely" many. The only thing that is inconsistent here is your usage of the concept infinity.

You can have a number that's arbitrarily large, though, right? Like, something that for the sake of argument is larger than any given value, but can still be treated as a real number. I think that might come in handy.

Although I know that doesn't preclude the existence of infinity. Seriously fuck these threads.

>larger than any given value
One number that is larger than any given value? No.
For any given value there exists a number larger than it? Yes.

After any NUMBER, there can only exist a larger NUMBER, provided there is no LARGEST NUMBER of which a NUMBER could not be larger.

Do you agree this is the claim?

I'm trying to prove that one doesn't exist only 0.99999999

I'll say if I agree when you write your claim in quantifiers about a well specified set of numbers so you don't pull the rug from under my feet and go "lellers I bet you didn't even realize that I use non-standard interpretations of these terms and now you agreed that infinity can't exist".

The only interpretation required is that of knowing english and being able to make logical connections.

>After any NUMBER, there can only exist a larger NUMBER, provided there is no LARGEST NUMBER of which a NUMBER could not be larger.
You agree this is the claim of infinity, and i'm sure you'll agree it is not an uncommon claim.

>After any number, there can always exist a larger number.
We can reliably know this to be true, if not true enough. If we said 99,999 was our example number, we can know in the very least that 100,000 is bigger and is too a number.

The only way to prove that a number exists where it cannot be incremented is to define a largest possible number. If everyone agreed 1 quintillion was the largest number, then once anyone reached 1 quintillion we would know to stop trying to add any more, so then we have a number that cannot have a larger number value relative to it. No one will recognize 1 quintillion + 1 has any real value, since 1 quintillion is already arbitrarily large enough to be useful for any real arithmetic. However, because we have a largest number the first part of the claim is no longer valid
>a larger real number exists after any real number
It's mostly accurate, but not perfectly accurate, so the claim must be altered.

But 1 quintillion isn't really the largest real number here in reality, so in our world the first part of the claim remains true and we agree that there is no largest real number, providing for the first part of the claim to always remain true.

>... provided there is no LARGEST NUMBER of which a NUMBER could not be larger.

The second part claims there can never be a largest number as such a number could not have a larger number after it, nullifying the first part of the claim.

Therefore infinity cannot be larger than any number as it would become the largest number, and if it truly weren't already treated as the largest number, infinity+1 wouldn't be seen as useless like like quintillion+1.

>You agree this is the claim of infinity
I don't agree to anything until you write the claim clearly in quantifiers about a specific set of numbers. Your game is the game of language tricks and intuition. Mathematics has replaced that by axioms and rigorous definitions because intuition doesn't work for these concepts.

As you can see, any prestablished definition FOR infinity cannot help but paradoxically state infinity does not exist, and i could prove this to you to a finite degree if you use any of the other various definitions prescribed to infinity, of which there are few and finitely many.

>sum of infinite series
I am too brainlet to grasp this

n=0;
while (x > 0){
n += 1;
Print(n);
}

This pseudocode is the equivalent of an infinitesum of +1 execution where every iteration partial sum is printed and readably knowable. Every print will always be a real number, and every print will always be larger than the previous print.
At no point will a print ever readout as [math]\infty[/math], therefore infinity doesn't exist as a number value.

If it doesn't exist as a number value, it cannot exist as a quantity. Infinity is then forced to exist by the sole definition of "never ending", even though the concept of never ending cannot be proven, but we could assume a base intent direction of it as "go and don't ever stop". With this being the only valid definition of infinity, to describe the pattern of 9's existing in 0.999... as "never ending, starting without stopping", then 0.999... can only ever equal itself and only itself at 0.999..., because anything more such as 1 would have brought some kind of end to what can only be endlessly unendable, where infinite sums cannot exist as objects but only as the values up to a real finite n'th limit because an unending, unendable limit of summation would never allow a result.

also dont be a faggot who cant read and thinks hes being tricked with words. You're only being tricked with numbers by choosing to believe infinity is rigorous or well defined. It isn't. Take it for granted that it isn't. At best it has one singular definition, that of unending work, yet few if any implements of infinity abide by this definition and instead treat it as an arbatrarirly large finite number where it's not infinite because it has no end, but instead because not enough information was provided to actually know what value it was. S h i t m a t h.

Put it this way, can you describe the exact difference between "an arbatrarily large real number" and "infinity", if infinity has a quantity value?

If i say to you "count from 0 to an arbatrarily large real number" and you agree to do so, do you think you'll respond with "which number?" If you did, i wouldn't tell you which number, i'd just repeat "an arbatraririly large real number".

This is the real trick that higher maths plays on you. In the realest sense of things, there is no different between infinity and the vague statement "an arbitrarily large real number", which means comparatively the quanitity of infinity IS an arbitrarily large real number.
You can't count to an arbitrarily large real number from 0 any more than you could count to infinity from 0. If infinity as a number and has a quanitity value, it is only as good as an arbatrarily large and undefined real number, and a vague undefined quanitity value is only as good as "???" Which means utilization of infinity would only be as realistically good as [math]\sum_{n=1}^{\rightarrow ???} \frac{1}{2^n}[/math] which is buttfucking retarded but literally exactly how it is used in calculus

>IF

X = 1;
IF (x=1){
>you're retarded
}
Yes, IF. What of it.

>infinitely large
>real number

pick one

I'm not saying infinity is a number, i'm saying it's "unending". Contrarily, infinity is used as a number in maths. You're not wrong, infinity isn't a number. I'm not wrong, infinity isn't a number. Maths is wrong though, because maths assumes infinity is a number, therefore mathematicians are wrong.

Infinity is a number, faggot. Just because it's not in [math]\mathbb{R}[/math] doesn't mean it's not a number.

[math]\overline{\mathbb{R}}, \widehat{\mathbb{R}}, \aleph_0, \omega, ...[/math], take your pick.

R is all real numbers. You're right, infinity isn't in R. Real numbers are all that matter. You need real numbers to do math. Math without real numbers isn't math.

>need real numbers to do math
>use infinity even though it isnt a real number
>pretend you're still doing math

>If an infinitely large arbitrary number can exist

It's your own fucking words.
retard liar

>Real numbers are all that matter. You need real numbers to do math. Math without real numbers isn't math.
t. never studied complex analysis
t. never studied DSP
t. never studied quantum mechanics
t. never studied QFT
t. complete brainlet

I was responding to a post talking about arbitrary numbers.

If infinity isn't a number, then an infinitely large arbitrary number doesn't exist. Any large arbitrary number could exist, but to be used as such they would have to actually be defined which number they are, as "arbitrary" is not useful in real number math. You can set up a situation where for any number, implicitly even arbitrarily large numbers, something can evaluate, but you must use a real number in these situations. You can't just leave the variable "an arbitrary number" remain undefined, it must be replaced with an actual real number to carry out arithmetic. "An arbitrary number" is used in place to describe any real number, even the numbers greater than any mentionable number. An arbatrarily large number can be any huge real number greater than any other mentioned number, but this only suffices as a variable awaiting replacement with a number. It has to be a number, it can't just remain undefined as "arbitrarily large".
There is a huge difference between getting the singular right answer in:
1 + x = 7
Versus getting the singular right answer in:
n + y = 8

There are innumerable ways to solve n+y=8, so how could you ever get the sole correct answers to the variables n and y? "There isn't enough information provided to properly solve it as intended." Is the only valid answer.

Using infinity in maths is the same exact thing as using an undefined, undefineable variable. You dont know the correct value of infinity no more than you know the actual sole correct value of n or y in n+y=8. You've left "infinity" undefined as "an arbitrarily large real number", forgetting to replace "an arbitrarily large real number" with an actual number value. If your limit is "an arbitrarily large real number", then you don't know when to stop. You don't know when that limit ends so you never stop, just identically the same as if the limit were infinity, ergo infinity = an arbitrarily large real number.

No field you just mentioned has real world value relative to physicality.
Enjoy learning fucking useless garbage where the only living you'll be able to make out of it is teaching it to college students who don't know any better but hope they're acquiring some useful information for their futures where probably none of them anticipate becoming teachers.

>No field you just mentioned has real world value relative to physicality.
confirmed brainlet

Ahuh, tell me, what has quantum field theory done for the world?
Quantum mechanics?
Surely something as early as complex analysis out to be useful.

Go on, i'm waiting.

>infinity = an arbitrarily large real number.

wolframalpha.com/input/?i=infinity
An unbounded quantity greater than every real number.

Infinity isn't a real number, by definition

protip: when you're in a hole, stop digging

youtu.be/gCAxGTt7nLg?t=8m

ITT.

A potential genius brings into question the meaning of numbers. Because he is a deep thinker.

Brainlets have no idea what he is talking about. Because they are brainlets.

I see you conveniently skipped DSP, cool. I know this is bait, but anyway:

en.wikipedia.org/wiki/Quantum_mechanics#Applications

By definition, it doesnt say what it is or isn't. It only says it is larger than any real number. This says nothing about infinity specifically, only its relation to something else. If it has no relation to real numbers, theres no point in mentioning real numbers. You are literally fucking retarded.

Yes, teaching it. Good job. Couldn't have fucked up that any better.

Maybe reread that link and actually learn how the things claimed to be derived from applications of quantum shit were actually invented before the field theories themselves.

Fuck the fuck off. You need quantum mechanics to make lasers and diodes work? No you fucking do not. Eat ass. You are literally a brainlet not because you tried to fill your brain with knowledge, but because you filled it with lies and retardations. Your brain is full just as much as would be required of someone who is intelligent, but it just happens to be full of nonsense instead of value.

>said the monkey of a book it couldn't read

>hand waving intensifies

>it is larger than any real number
if infinity were a real number,
by definition it would be bigger than itself

lrn2read

>Maybe reread that link and actually learn how the things claimed to be derived from applications of quantum shit were actually invented before the field theories themselves.
Sorry to break it to ya, but lasers and LEDs were invented after QM.
en.wikipedia.org/wiki/Quantum_mechanics#Electronics

>You need quantum mechanics to make lasers and diodes work? No you fucking do not.
Yes you do.

>Eat ass. You are literally a brainlet not because you tried to fill your brain with knowledge, but because you filled it with lies and retardations. Your brain is full just as much as would be required of someone who is intelligent, but it just happens to be full of nonsense instead of value.
k.

n = n+1

[math]\sum_{n=1}^{n+1}[/math]
Here's your "unending" operation. Heres how it should read. Easy. At n=1, the limit is 2. At n=2, the limit is 3. At n=3, the limit is 4. There you go. No infinity required, as a number or even a word to describe, and certainly not required as a symbol.

>Look at me i'm fucking isaac newton i'm a goddamned brainlet I GIVE THEE CALCULUS

>No infinity required
then it's finite

>yawn

Oh gee willickers, boys, we got ourselves one of them thinkers! An unending operation is finite! What an amazing analysis!
I guess since 0.999... has unending 9's in it, must mean there are a finite amount of 9's in it!
Don't even try asshole, 2/10.

>0.999...
has an infinite amount of 9's

not a finite amount
>infinity needed
>mind blown

as long as n is a real number that's finite
replace n with inf, now you've got an infinite result

infinity is required

It is when you look out.
Eternity lies within.

Infinite = unending
You assume "unending = finite"
Therefore infinite=finite, by your logic.
Unfortunately it's arbitrarily finite, meaning undefined and vague, so you cant increment from n=1 to n=infinity, unless you decide to change the sum's limit at some arbitrary point from n+1 to simply just n, stopping the unending work, but if its no longer unending, its no longer finite, and therefore no longer infinite.

Golly, its almost like it is literally impossible to use infinity properly. Fuck quantum mechanics, this is the true unknown for the ages. Every time someone tries to define infinity by a associating it with a number, it simply changes its own definition and can't be used!

>infinite=finite, by your logic.
nope

any n is a real number
infinity isn't

The only way you can get to infinity
is inserting infinity instead of n
Which just defeats the purpose.

The development of lasers needed masers to be developed. The development of masers relied on heating gasses. If increasing the temperature of a gas qualifies as quantum mechanics, then Hank Hill has a Ph.D in quantum mechanics. Unfortunately with such a shit field of useless knowledge, Hank Hill makes minimum wage selling barbecues instead of doing anything worthwhile for society.

The idea that masers would produce yielding results in analyzing hyperfine bullshit to 20 gigahertz is also bullshit. Atomic clocks aren't real. The tech to measure the oscillation value of ceasium-133 didn't even exist til the 90's, despite the atomic second coming about in the late 60's. At best it could have only been theoretically possible to predict using some made up form of uncheckable math what the hyperfine oscillation of caesium-133 could be, not realistically checkable and proveable. Worse yet that since the second were defined as however many gigahertz of radiation from caesium-133, this now invalidates the second because 1hertz = 1second. As if infinity being useless wasn't bad enough, the SI second is actually based on a value that required the second to have already been defined as something else. What fucking good is calling the second as "9 billion cycles per second"

Holy fuck. God exists but he did not make man. Nothing as dumb as man ought to be.

>Hank Hill has a Ph.D
>Atomic clocks aren't real
>1hertz = 1second
>God exists but he did not make man
KEK

>The development of lasers needed masers to be developed. The development of masers relied on heating gasses. If increasing the temperature of a gas qualifies as quantum mechanics...
non-sequitur

Just because infinity isn't a real or natural number doesn't mean infinity can't exist. Infinity isn't a single concept but a collection of concepts. Saying a series equals infinity (in the extended reals) is saying the partial sums have no upper bound. You also clearly agree that the set of natural numbers exists and that it has no upper bound as for every natural number n there is a successor number n+1, what is the size of that set? That's another way the concept of infinity manifests itself.

Laser Light in which medium?
Light itself has no temperature, step up your unambiguity game.

Yes, you're right. infinity is a concept, not an implement, not a construct. If it were as simple as using concepts to define reality, all my conceptual game ideas would have already made me wealthy - i don't have to actually develop and market the games cause the concepts are just as good.

Protip, using a word attributed to vagueness to attempt describing something else as anything but vague is dumb.

The concept gives rise to different but related constructs that are well defined and don't lead to contradictions if you stick to the definitions. You refuse to do that and instead you handwave silly arguments based on intuition.

>Saying there are an infinite, non-finite amount of parts between finite 1 and finite 2 means you can never reach 2 from 1 by incrementing in those parts.
You can by doing infinite increments. This is just the same old Xeno's paradox fallacy. You're crossing infinite increments whenever you take a step, because each increment takes an infinitesimal amount of time to step over. But again, this doesn't even respond to the point since no one is computing the sum by adding each part incrementally. They are transforming that sum into something else. You didn't respond to anything I said, retard.

>After any real NUMBER, there can only exist a larger real NUMBER, provided there is no LARGEST real NUMBER of which a real NUMBER could not be larger.
FTFY

Temperature is always a measure of average translational kinetic energy so kindly fuck off. There is no such thing as negative kelvin as by definition 0 K equates to zero-point energy, the lowest possible energy a system can have under any circumstances.

>Every print will always be a real number, and every print will always be larger than the previous print.
>At no point will a print ever readout as ∞∞, therefore infinity doesn't exist as a number value.
Notice how you switched from "real number" to "number." Time to go learn elementary school math.

>Put it this way, can you describe the exact difference between "an arbatrarily large real number" and "infinity", if infinity has a quantity value?
What is a "quantity value"? Can you stop making up terms and just write a real argument. Because so far your argument doesn't exist. Oh and the difference is that the former is finite while the latter is not.

en.wikipedia.org/wiki/Negative_temperature

i like infinity

i didnt use to get it before

now i get some of it

its great

Do you guys want to know what I think?

No.

Xenos paradoxes include assumed finite elements. So no. Think again
Die in a tire fire you fucking retarded ESL loser.

>Xenos paradoxes include assumed finite elements.
Yeah a finite length divided into infinite increments you utter tard. You clearly have no response.

You're missing that the arrow paradox assumes an infinite quantity of freeze frames of an arrow in flight constitute the entire path of the arrow in flight, despite that no freeze frame is distinguishable from another because he assumes 0 time has passed between any frame.
Aka the retard would let that [math]0 × \stackrel{n}{\infty} > 0 [/math], n added to denote he's referencing the number infinity and not the "never ending, non-numerical increment" act of "infinitely" repetitive or increasing.
Since 0 × n = 0, he obviously had a misconception. Staring at a photo of an arrow in flight will never suddenly turn the photo into an animation showing where the arrow flies to, no matter how much time passes while having stared at the photo, nor does copying the photo innumerable times and arranging them in a flipbook allow the arrows flightpath to be animated.

The point is, you cannot make it to 2 from 1 in infinite increments unless you assume to abide by xeno's logic that 0×infinity > 0 [if not 0×infinity = 1], and if you assume this is the case then the utmost infinite'th partial sum of 1/2^n (achilles and tortoise) at n=infinity is [math]\frac{1}{\infty} = +0[/math], meaning the final required partial sum to sum totality is 0.
Extend this to 9/10^n, and at the infinite'th n, the infinite'th digit is 0, giving 0.999...0, where the "infinite repetition" is terminated by a 0 which prevents rounding up and also uniquely seperates the value with proper termination from 1.0 which could just as easily be written as 1.000...

To elaborate in solution, [math]\sum_{n=1}^{x} \frac{9}{10^n} = 0.9999[/math]
n=1: 0.9
n=2: 0.99 (+0.09)
n=3: 0.999 (+0.009)
n=4: 0.9999 (+0.0009); x=4, four nines
Provides evidence that the final partial sum must be a significant non-zero value to sum totality, but 1/∞ = 0 forces the final partial sum to be a value that cannot add anything extra to the sum in totality, providing for 1/2^n = 1 for any arbitrary n less than infinity.

>the infinite'th digit is 0, giving 0.999...0,

they're all 9's, cut the crap