/sci/ - Science & Math

>>7347916
1+1 = 2
2+1 = 3
and so on

In a universe, there can only be one infinity. And that object is either stupendously big, or very very very very small. There are a finite number of stars in an infinite universe, which allows for more numbers to appear by breaking up the star while still not crossing boundaries. Sorry for the shitpost op, but you asked for it by making this thread.

>>7347969
>There are a finite number of stars in an infinite universe

>>7347916
math is all about abstract concepts and sure, infinity is one of them and it doesn't necessarily exist irl
whether our universe is infinite is unknown/unknowable and it's pointless to debate it. You can create hypotheses of your own, sure, it's called philosophy

>>7347969
the fuck?

>>7347916
My best guess at an intuitive interpretation of infinity is the following:

Start with the concept that a physical system with a desired precision can have parameters pushed to a certain limit beyond which the system no longer appears to change (for the given precision)
This can probably actually be written out formally and a critical value for the result could be found.

Then extend that idea into pure mathematics by allowing that system to take on arbitrarily high precision.
Solving for that critical value of the result is then (I think) equivalent to solving for the limit as the parameter approaches infinity.

In other words, what I think infinity is, is a mathematical abstraction for systems that have arbitrarily high precision.

>>7347916

lim x->0 ln x = -infinity

proof...
This limit can only be true if and of if it follows statement below
0< |x-a| < δ ⇒ f(x) < N
0 < |x| < δ ⇒ ln x < N

ln x < N ⇔ 0<|x|<e^N
∴ δ = e^M
|x| < δ
|x| < e^N
|ln x| < ln(e^N)
ln x < N

Hence ln x < N
Therfore the lim x-> 0 ln x = -infinity is true. Which means infinity exists.

>>7347916
But it is an abstract concept. It's the notion of a process going on indefinitely. For instance, take any number and divide it by 2. Take the result and divide that by 2, and so on. If you only keep on dividing, what happens? This is a type of question that can be answered with the notion of infinity as a tool. You will notice that as you divide indefinitely you will always get some number smaller than the one before, but never zero. In this example, zero is the limit as the process goes to infinity. That is to say, keep on dividing as many times as you'd like and you can get as close to zero as you want.

It's not really something that needs to be proven to "exist". You don't need to *actually* divide an infinite number of times in the example above in order to see what happens *if* you would.

I think the simplest way to think about it in the context of mathematics is that if you draw a line on a piece of paper, you can decide for yourself and for your own purposes how to interpret the length of that line. That is, you can decide it has length 1, or length 0.1 or 0.00001 and go from there. In this way, it is possible to "zoom in" indefinitely into the number line, since there is no smallest number (you can always add more decimals). On the other side of the scale, it is always possible to add (or subtract) indefinitely from any given number, so that the number line stretches into infinity, since there is no set limit on how big numbers can be.

Does this mean that infinity "exists", makes sense or is an applicable notion in any field of study? No, because in reality there are always constraints. But if our number system didn't work this way, it wouldn't be the convenient and abstract tool that it now is.

>>7347993
Using math to prove that infinity is a valid mathematical concept does not prove that anything in the real world is infinite.

>>7347997
oh i didn't set out to prove that infinity exists in the "real world" whatever that means. the term "real world" in itself is an abstract concept that requires definition. I only set out to prove that mathematically, infinity exists using limits.

>>7348002
I think OP was really asking if there is any physical quantity that is known to be infinite.

>>7348008
>if there is any physical quantity that is known to be infinite
or perhaps I should say "any physical observable" or something, since infinity isn't a quantity.

>>7348008
Well if he did want to know if there is a quantity that is infinite, then there is not. Because definition, a quantity is not infinite. It is contradictory to say a quantity of something is infinite. It just doesn't make sense. So to answer OP's question, no. There is no physical quantity that is infinite but that doesn't mean infinity doesn't exist. It does exist.

There are an infinite amount of numbers between 1 and 2

>1<1.000000000000000000000000000001<2
>1<1.000000000000000000000000000002<2
>etc

>>7348017
>>7348017
Actually scratch that. Theoretically there is a physical infinity. Maybe some physicists can correct me if I am wrong but as a particle approaches the speed of light, does the particle not have infinite mass? I'm not quite sure but either the particle has infinite mass or infinite energy. But that is probably the only infinity that you could probably see in reality...

>>7348017
OP here - show me a physical and observable infinity then.

I heard Hawkings said something that it's like a sphere.

Universe is continuously expanding. What we've observed is less than 5% of its expected size. It's tremendously large by any conceivable human notions.

It is expanding into... something. That something within which it is contained, is infinity.

>>7348030
It is not expanding into something in the way that liquid expands to assume the shape of a container. In fact, the textbook I read said that it is misleading to use the phrase "the universe is expanding". Its just the distances between everything, in particular the galaxies is expanding.

>>7348032
I'm trying to explain from a human notion of things contained within things. What I'm trying to get at is that the idea of infinity, while an abstract one in itself, can be used to represent anything in a system that is inexplicable within the framework of that system.

The idea that there is a universe full of matter and energy growing in size, isn't explainable if we ignore the "space" outside this universe. But we have no notion or basis for that space, let alone figure out what in turn contains this space. It's a recursive exercise. That idea is infinity.

Also, the phrase the universe is expanding is not misleading. The distance between the stars and galaxies is increasing, being filled with this weird "void". We don't know that this void is, so we call it dark matter. There is no evidence to suggest that the void itself didn't come from the big bang along with all the stardust.

>>7347916

There's an infinite number of points between two points in space.
See xeno's paradox.

>>7348027
>OP here - show me a physical and observable infinity then.
He just said that exactly that didn't exist in the post you responded to

>>7348041
There is actually no evidence of that

>>7348044
> asking for evidence of real numbers

I'm out.

>>7348052
good
the reading comprehension level of the thread will probably be higher without you

>>7348027
The number of times you can go around a circle before you reach the end.

>>7347916
>implying any number or mathematical concept "exists"
platonist pls go

It's hard to say. Technically, if space exists as a continuum, then the number of states an object can occupy is infinite.
In fact, there'd even be an infinite number of places in between each of them. Like, just moving your hand an INCH means you've moved through uncountably infinite places in between.

But we currently don't know whether or not space is quantized.

>>7347916
There's an infinite amount of time in this universe.

/thread

>>7348022
The mass of the particle approaches infinity as it approaches the speed of light. It doesn't get there though. And this is only true for massed particles.

>>7348022
No it would need infinite energy, not mass. Protons are assumed to have no mass not an infinite store

>>7348765
Mass is equivalent to energy you dingus.

>>7348763
I understand it is only true for massed particles. But is the mass of this particle not defined at c? Is it asymptotic at c?

>>7348765
>protons are assumed to have no mass

wh-what?

>>7347916

It would take an infinite amount of time for a hypothetical single immortal person to read all the books written on every single subject like history, anthropology, physics, math, literature...etc and also every post on the internet since it was created, and listen to every audiobook, song, see every piece of art, an infinite amount of time to experience pretty much all of the things created by humans, because the human population keeps increasing and many more people are becoming educated, more people keep creating things every second, the rate of creation is much faster than the fastest rate possible of a single person consuming it.

>>7348779
Massed particles can't reach c. They don't physically exist.

>>7348869

Also:

"The path integral formulation of quantum mechanics is a description of quantum theory which generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique trajectory for a system with a sum, or functional integral, over an infinity of possible trajectories to compute a quantum amplitude."

Infinity of possible trajectories of a quantum system

there is an infinite number of faggots on this board

there is no need of evidence

it's an observable fact

human greed is infinite

>>7349195
deep