/sci/ - Science & Math

> inb4 a thousand high school kids who think math is a religion spout the sermons of their teachers, infinity is a concept not a number etc
> inb4 numbers are concepts etc
it's a symbol with various meanings in various contexts, it's hard to say more than that without choosing a context

think of infinity like another dimension

>>5408541
So research into said contexts is the way to go?
Thanks for legitimate response

>>5408541
>sermons of their teachers, infinity is a concept not a number etc
so you're a freshman who thinks everyone else is in highschool?

>>5408556
It's not a symbol that is given a consistent interpretation in all its uses. In some cases it means one thing, in others, another. It is often taken to mean "unbounded" but in other cases it is given an actual meaning as a point in a plane. In some cases you can treat it as a number, but then you lose some convenient properties (like the system which includes it is no longer a field).

In some cases even the symbol is disregarded but the concept of "unboundedness" is also disregarded and given some other kind of interpretation like infinite cardinals and infinite ordinals.

It's a fucking huge topic.

>>5408519
>If it does exist why can't a value be assigned to it?
What exact value do you propose we assign to infinity?
>999999999999999?
>999999999999999999999999999?
>99999999999999999999999999999999999999999?
>99999999999999999^99999999999999999999999?

In analysis, infinity means as big as you need/want/like/choose.
In set theory, there are different kinds of infinite cardinals :

>countable sets
each element of the set can be assigned to a unique natural number.

>uncountable sets
there are too many elements in this set to have an bijection with the natural numbers. The set of the real numbers is uncountable.

>>5408519
Infinities CAN be assigned different "values"; they're called limits.

>>5408579
/thread

>>5408519
Don't think of "infinity" without any context. There are a bunch of different concepts called "infinity", and they all get conflated in English.

Instead, here's a particular example: Consider the set of natural numbers, i.e., 0, 1, 2, 3, 4, etc. Now, how many such numbers are there? Well, it certainly can't be finite, because you can always add one to get a bigger number, so it's bigger than every finite set. Therefore, if you consider the whole set of natural numbers, it's infinite.

It turns out that there are different sizes of infinity; the natural numbers are the smallest infinite size. (The rational numbers are also that same size, while the real numbers are strictly larger.) But if you're still having trouble with infinity it general, don't worry about that yet.

As for whether infinity "exists"... Do numbers exist? How about perfect circles or lines? Mathematical concepts tend to be grounded to some extent in physically observed patterns in the universe, but they aren't material objects, so it's hard to say what it even means for them to "exist".

>>5408557
No, I've just argued with such deluded thinkers here on /sci/.

>>5408574
Haha, alright

>>5408576
Note my overall confusion

>>5408578
So the reoccurring theme throughout this thread is "not a simple answer" and that it is something that envelops many things?

>>5408576
<span class="math">/aleph_0<span class="math">[/spoiler][/spoiler]

It is not a value. It's a concept; an idea.

>>5408589
> because you can always add one to get a bigger number
faith-based mathematics

>>5408576
<span class="deadlink">>>5408595[/spoiler]
oophs
<span class="math">\aleph_0[/spoiler]

>>5408589
Helps a lot, thank you.

>>5408599
What, are you an ultrafinitist or something? It's a straightforward consequence of the Peano axioms that repeated application of the successor operation produces distinct numbers.

>>5408608
> it's a straightforward consequence of Peano axioms
You or me or anyone being able to do something is not a consequence of any formal axiomatic system.

>>5408612
Okay, I didn't literally mean "you can actually carry out the process of adding one arbitrarily many times". I realize there are physical limitations on such calculations.

I figured it was understood that I was talking about the consequences of a formal system. You're free to interpret those consequences as meaningless manipulation of formal symbols if you so choose — that's accurate on some level — but I find it more intuitive and productive to talk about it as though it corresponds to some reality, regardless of whether it "actually does" (whatever that would mean).

>>5408612
i hear ya man

just the other day i divided by zero just to stick it to the man

>>5408621
> I figured it was understood that I was talking about the consequences of a formal system.
And who would work them out? God?

>>5408652
What assumptions do you reject, then? Is any form of indirect reasoning acceptable, or do you have to actually count everything one by one before you'll believe in it?

The formal proofs of the relevant facts in Peano arithmetic are quite finite and comprehensible (though rather dry), and I don't see why those aren't sufficient.

>>5408597
all numbers are ideas.
and they are all nonsensical without a context.
on a very basic level, 1= stone, 1+1=2 stones, but this only makes sense if our unit of analysis is vague enough to disregard the weight dereference, chemical make-up, molecular count, and an myriad of other things. we adopt the idea that stone exists and represent it with a symbol of "1".
the fact that there can never be a second stone identical to the first doesn't matter because the concepts of "1" and "+" are so useful in helping us think and organise our thoughts of the universe. the same goes for the concept of infinity.
So in number sets, yes infinite means always growing cause we can always +1.
but are numbers infinite? NO, because eventually the universe and all time will cease to exist and so a number counting machine would reach the largest actual and finite number it could before vanishing.
or to baby step you to the concept, ask yourself if + exists?

>>5408672
> or do you have to actually count everything one by one before you'll believe in it?
If you tell me that a formal system which suggests this is how numbers and arithmetic are defined is a good one then I would suggest that indeed we should count them one by one. Indirect reasoning is not a problem. Induction isn't a problem. The successor function is not a problem. I have no problems. But if you tell me, this is arithmetic, then I will have no qualms saying that, for instance, <span class="math">10^{10^{10}}[/spoiler] "doesn't exist" and you definitely cannot reduce this to the first principles.

>>5408693
sauce?

>>5408732
a slightly hungover conversation with my first calculus teacher. (retuning to school after dropping out as a child). now i really wish i had drunken less that evening or drank with him more, he had strange way of explaining things. so admittedly, its a theory i heard that works for my understanding but maybe its complete turd, and its only highlights here . im interested
if you have anything to add or refute, as its been rolling around in my head a while

>>5408758
I meant the picture

>>5408693

Does + exist?

Pick one of the alternatives:

>words exist and have meanings
>words don't exist and/or don't have meanings

>>5408770
lol. I googled "rock boobs" images

>>5408773
unicorn
word exists and has meaning
plus
word exists and has meaning
neither is tangible
my post was about "1" "+" and "∞" are all concepts of intangibles.
OP asked ">Does it not exist?"
I thought if she thought carefully on what it means for + to exist then understanding of ∞ would be easier

>>5408519
>If it does exist
It doesn't, so don't worry about it.
It's a vague buzzword (in Mathematics) for the more-precise concept of an "unbounded" and "unlimited" arbitrarily-large quantity. In other disciplines, it's even more vague, often to the point of being meaningless, as in philosophy and theology.

ITT: high schoolers think they know math