/sci/ - Science & Math

Infinity is just a concept.

It is not a real thing that you can add together like two apples.

>>5684276
Nice attempt at obfuscation, but we do not add two "apples", we add 1 + 1. So the correct analogy would have been:

"It's not a real thing you can add together like 1 + 1 = 2"

But of course, 1 and 2 are just "concepts", they're not real things. They're abstract symbols.

>>5684276
Retard.

http://en.wikipedia.org/wiki/Extended_reals#Arithmetic_operations

>>5684276
Numbers are just a concept.

It is not a real thing that you can add together like two apples.

ITT: raging torn from reality math nerds

>>5684281
That's just formalism.

One problem with your proof: The Commutative Property of Addition

>>5684284
ITT: raging torn from reality math nerds with $500K starting.

>>5684292
That's not a problem with the proof. What you mean to say is that it's a problem with the conclusion. Please think a bit clearer.

But in fact it is not a problem. We simply conclude that the commutative property of addition only holds for finite additions.

2 + 3 means

M < N < A < B < C

which is also 5, so 2 + 3 = 3 + 2. And you can easily verify that commutativity holds for any finite sum. So there is no contradiction with "classical addition".

4/10 OP

>>5684288
>math
>$500K starting

Infinity isn't really a number.

>>5684280
confirmed troll.
2/10 because i feel bad you took the time to post

>babby's first misunderstanding of infinity

OP this is one of those 'proofs' where in the start, you need to ask yourself: 'Is my intended proof so blatantly obvious to everyone who has finished grade school, that maybe everyone has thought about it and before I venture into this proof, I should google it!'

>>5684311
You're the only troll here. You got 3 separate responses telling you that you were wrong. Rather than confronting your intellectual inadequacy at constructing a reasoned counterargument to these comments, you tried to make the issue go away by pretending everybody else was being intentionally stupid. Talk about sour grapes. Just depressing, really. Please stay out of my thread (unless you want to talk rationally).

>>5684282
Yeah but we can prove their existence through physical means, i.e 2 apples. So stop being a troll and fuck off back to /b/

A < B < C < D < E < F < ... < α

is the same as

α < A < B < C < D < E < F < ...

with the arbitrary symbols renamed

>>5684321
If the flaw were so obvious, I wonder why you didn't just point out where it is.

You're just engaging in exactly the dogmatic behaviour I mentioned at the beginning. You're the one with the preschool understanding of math if you don't know that math is based on proofs, not assertions.

>>5684335
> prove their existence through physical means
> mathematics

Are you joking?

Do you think people establish the axioms of group theory "through physical means"?

Pure mathematics is an abstract science.

>>5684337
Thanks for a decent response at last.

But which symbol in the second sequence corresponds to the last symbol in the first sequence?

If you can add 1 to it, it isn't infinity.

I stopped reading when you implied M is the 5th letter in the alphabet

>>5684352
You're saying the even numbers aren't an infinite set because you can add the number "1" to the set?

>>5684270
>edgy
>Not on /b/

You're wasting your potential, kid

>>5684358
I don't think you ever started reading, because I never implied that.

The letter are arbitrary. You could use any symbols. I could have said 3 corresponds to

& < @ < #.

All that matters is the order.

Have you never done algebra before? You can call the variables anything you want, it doesn't change the math.

Of course ∞ + 1 > ∞, that's trivial. On the other hand, we do have 1 + ∞ = ∞.

>>5684359
You can add the number 1 to any known number within the set. You can't add 1 to the set because the set is just a categorical descriptor that allows you to determine if a thing is even or not. The point of infinity is that it isn't finite. There is nothing greater than it and there is no approaching it. If you have twenty million of something you're no closer to an infinite number than someone with zero of that thing.

>>5684370

There are the same number of even numbers as there are counting numbers. The proof of that is on the Internets. Your entire premise is ignorant.

Doesn't work because 3 + 2 = 5 and 2 + 3 = 5, BUT M and N do not come before A, B, and C.

>>5684371
What are you talking about..?

X = "the positive even numbers"
Y = "the positive even numbers and the number 1"

X = { 2, 4, 6, ... }, Y = { 1, 2, 4, 6, ... }.

Y = X U {1}. Y is the set X with the element 1 added to it. Your objection that this is "impossible" is philosophical mumbo jumbo.

Also it doesn't make sense to represent 1 as A and α.

>>5684372
So you're saying my proof is correct?

>>5684386
The letters are unimportant. All that matters is the order. What you're saying is akin to saying it doesn't make sense to talk of 1 apple and 1 cow. Yes it does. 3 refers to

A < B < C

and equally

X < Y < Z.

They're just symbols. It's the order, <, which matters.

>>5684387
>Philosophy
>Mumbo jumbo
Everyone can safely ignore you now.

>>5684389

Your proof is poo-poo.

Thanks for wasting our time.

Best Fishes.

>>5684383
Care to explain? I don't know what you mean. Ignore the canonical order of the alphabet, I am not using it. I am just using the symbols of the latin alphabet. M and N do come before A, B, and C if you define it to be so.

>>5684389
I haven't read your proof.

>>5684399
On sci? I don't think you'll find many people agreeing with you actually.

>>5684397
If the order of the letters don't matter then it doesn't matter whether 1 comes before 3 and your whole point about 3 being third and 2 being second is pointless.

>>5684401
Please do.

But you're saying my conclusion is right, at least?

>>5684409

Again. Your conclusion is wrong.

Aleph-Null is the Cardinality of the Integers,
of the even Integers, of the Primes.

Aleph-Null + Aleph-Null = Aleph-Null.

>>5684403
Numbers are not arbitrary. I didn't use numbers as symbols because it would confuse the whole thing. I only used letters as arbitrary symbols.

3 represents

A < B < C

where the letter are arbitrary.

2 represents

M < N

where the letters are arbitrary.

2 and 3 are not the same thing.

>>5684409
Sure. I don't know why that's relevant, though.

i though only people who study philosophy argue about shit like this.
OP you do know some infinities are bigger than others?
even if this is all correct whats the point?
where is the inf +1 application

which means that "infinite numbers" aren't naturals

good job now read some cantor

>>5684413
>2 and 3 are not the same thing.

Then 2 and 3 does not equal 5.

>>5684416
You've obviously never met a set theorist. Or followed a babby tier course on set theory. Or have ever been near math ever in your life ever.

>>5684343
Well,

A < B < C < D < E < F < ... < α

would be the wrong way to express

A < B < C < D < E < F < ...

plus α

because you would just add it to the left side instead of the right side

So, no additive identity guys?

>>5684421
studin applied math :/
ye i did some baby set courses some topology but son this argument is invalid

>>5684337
Those two things aren't order isomorphic. So no.

>>5684270
Congratulations, OP! You've just rediscovered ordinal numbers.
https://en.wikipedia.org/wiki/Ordinal_number
This is an important and well-studied concept in set theory. Note that the letter ω is usually used in place of ∞, to avoid confusion with other notions of infinity. Ordinal numbers generalize the concept of counting, and so, rather naturally, ω + 1 > ω.

However, there's another type of infinity: cardinal numbers. Cardinal numbers generalize the concept of size of a set, and therefore, adding 1 to an infinite cardinal doesn't make it any bigger. The difference is because ordinal numbers care about order — for example, 1 + ω = ω, but ω + 1 ≠ ω — while cardinal numbers don't.
http://en.wikipedia.org/wiki/Cardinal_number

>>5684415
The OP's assertion being right is obviously rather relevant to the OP's thread, where a large number of dummies are saying it's wrong, e.g.

>>5684414

and it would be helpful if you could explain to them why they are wrong. Though I doubt you'll have much luck, even a mathematical proof isn't enough to convince them.

>>5684429
Wow! So you're telling me all of the people saying I was talking nonsense were in fact just ignoring my reasoning and dogmatically regurgitating their high school lessons, after all?

These numbers sound cool.

infinity =/= a
a + 1 > a
You cannot represent infinity as a variable. Neither can you add one to infinity.

>>5684437
so fucking edgy

>>5684437
Eh... well, the way you phrased it wasn't very formal, so it'd be easy to mistake it for some common misconceptions about infinity. There are several different mathematical concepts that all get called "infinity" in plain English, which is why it's important to be clear about which. (With cardinal numbers or the extended real line, what you said is completely false. Strictly within the real numbers, it's nonsense. With ordinal numbers, it's true. That's why precise terminology is important.)

Talking about "infinity add one" makes just as much sense as "blue add one". It's a concept, rather than a physical number.

>>5684450
>a physical number

>>5684453
>i am a le shitposting tripfag

>>5684453

>adolescent illustration

>>5684456
Ironic shitposting is still shitposting. Don't do it.

>>5684456
He's right though, your comment was a colossal failure. All numbers are "concepts", not "physical".

>>5684438
Wow. You don't know what a variable is.

Clue: they can vary.

>>5684463
Serious question here,
Why can't numbers be a physical thing?

>>5684490
Because you can't have multiple two's in your hand, you can have multiple apples in your hands. The amount of apples can be described using a number, but they aren't a number themselves, they are apples. Numbers are a thought or descriptive technique used to describe an amount of something physical. Though this is only with natural numbers, all the other number sets are completely theoretical and cannot be tied to a physical object rationally.

>>5684490
Why can't "clockwise" be a physical thing?
It's an adjective, not a noun.

is op trying to say that some infinities are larger than other infinities? because that's true

>>5684523
It is true but not in this case since we're dealing with the same kind of infinity.

>>5684518
Well, one could say that any physical "thing" is just a property of energy, so an atom is as physical as a number in this case, it's not an actual "thing" it's more of a name we give to a region in space with certain numerical properties like mass and charge.

This is exactly the kind of thread one would make if one had just learned about ordinal arithmetic and were inspired use it to troll idiots on /sci/.

>>5684338
>pure mathematics
>any kind of science at all

It doesn't follow any of the scientific method. It is not a science. Hence this board is called "Science & Math," not just "Science"

I'm convinced.
A nice consequence of this proof is that I actually won all those arguments as a kid.

>>5685156
> being this tied up in semantics

This is an awful lot of work to put into a troll. And it still sucks.

>>5685181
> being this wrong

>>5685186
> completely semantic claims
> having truth values

you sure you're a scientist..?

>>5685193
> Not being able to follow basic logic

you sure you're a mathematician.. ?

>>5685207
> can't into definitions
> thinks he can into logic

>>5685220
>2013
>implying definitions aren't artificial

>>5685220
> Science: Systematic knowledge of the physical or material world gained through observation and experimentation.

u wot m8

>>5685226
> implying they aren't
> wait what
> ...
> implying you've forgotten what you were arguing in the first place

>>5685229
Words have multiple definitions.

It is quite amazing to me that this is news to people.

>>5685243
Keep being that proud minority. Maybe someday you'll realize how the world works. Probably not.

>where α is (by definition) after all of the Roman letters. So as a matter of fact α is higher than all of the numbers in ∞.

>where α is (by definition) after all of the Roman letters.

>after all of the Roman letters

>after all

it is infinity. there is no all. it can't be placed "after all the Roman letters" because they would not end.

endlessness=endlessness no matter what you do to it, because if it is truly endless, then it cannot become less or more, it will only remain endless. one endless stream cannot be more endless than another.

>>5685307
There's no problem with referring to "all" of an infinite set.

For example, we refer to N as the set of "all positive integers".

And there's no problem with defining a relation on an infinite set. For example, 0 is less than all of the elements of N, isn't it? Given an element of N, it will be bigger than 0.

What's the problem?

>>5685307
α, as he has defined it, is usually called ω, and ω+1 > ω.
Ordinal numbers, yo!

>>5685316
0 isn't a number. it is nothing. when saying N>0 you're only saying something is more than nothing. that is not a relation, that is whether something is or isn't, exists or does not exist

>>5685334
> 0 isn't a number

1/10, back to troll school you go.

>>5684270
but infinity plus one is still infinity, and nothing is greater than infinity, even infinity.

op the statement in your pic is false

>>5685339
its not, its the absence of a number. you cannot have 0 things, since there is nothing to be had.

>>5685348
You can't have pi of things either, is that not a number? How about e? You can't have sqrt(2) of things, is that also not a number?

>>5685348
http://en.wikipedia.org/wiki/0_(number)

>>5684288
used to be $300k starting, are all the math majors getting jobs in canada now?

>>5685362
inflation due to all the math phd's running the economy

>Adding a number to a concept
>Expecting the answer to be expressible as a number
>2013
>ISHYGDDT

>>5685849
This whole "infinity is just a concept" cliche is a decent simplification to deter grade schoolers from using naive intuition about the infinite, but it really doesn't belong in a serious mathematical discussion.

Of course infinity is "just a concept"; so are all mathematical objects! It doesn't make a shred of difference when we're talking about something like ordinal arithmetic, where addition, multiplication, and exponentiation of both finite and infinite ordinals is a rigorously defined operation.

idiot OP. addition is commutative.

>>5684270
∞+1=1+∞

There. I solved the equation.

>>5684317
The first of many. Cute!

OP if you want people to listen to you stop fucking ranting about dogma and acting like you're TEARING DOWN THE FOUNDATIONS OF THE ESTABLISHMENT instead of putting forth a conjecture

People will be less defensive if you don't preemptively call them retards and put yourself on a pedestal. You're engaging in crank behavior.

>>5686305
This. When I'm called an idiot blindly sticking to some dogma I don't read what comes next.

>>5686314
and it's annoying as shit because it's circular reasoning and a self-fulfilling prophecy

>call everyone blind, dogmatic idiots
>they ignore you because you're acting crazy and rude
>SEE LOOK THEY REFUSE TO CONSIDER MY POINT OF VIEW

>>5686326
Yeah, that's how conspiracy theories work too. Come to think of it, most cranks are probably conspiracy theorists who read a few Wikipedia articles on number theory and never looked back.

100 replies to someone treating infinity as a number LÖL

>>5686396
If I can treat n mod 7 as a number I can sure as fuck treat infinity as a number.

>>5686441
lel

>>5684270
Abstract thoughts without prove are just that, thoughts/imagination.

I can too reason for existence of something just because it might exist. But by doing so I justify every other imagination as a fact as well just because it MIGHT exist.

>>5684270
0/1000

>>5686441
Which inifinity?

There are already a shit ton of different infinites, with a shit-ton of well know properties.

How fucking old are you? Trollin?

http://en.wikipedia.org/wiki/Georg_Cantor

first of all your proof is just semantics not math
secondly nobody claims inf+1=inf
we know some infinities are larger than others, look up on cardinality of uncountable sets and proof of Cantor perhaps

/b/ wasn't able to help with this geometric optics problem so I thought I'd come to /sci/. What are your thoughts?https://docs.google.com/file/d/0B1C1OxMibhcodXU3Y3hFdFZXQkk/edit?pli=1

>>5686201
Addition and multiplication of cardinal numbers are commutative. Addition and multiplication of ordinal numbers are noncommutative.

>>5686556
If "inf" is any infinite cardinal number, then inf + 1 = inf is actually true. You can't reach higher cardinalities using addition or multiplication. However, adding 1 on the right always gives a larger ordinal number.

>>5685307
Yes, yes it can be more endless.

It can.

Take the set of rational numbers. like 1,666 ; 1,77777777 ; 1,5566666

(just examples)

Take the set of irrational numbers, like PI, 1,784241189 ; 2,786123 ; 9,18612315


The set of irrational numbers and rational numbers are infinite.

But there are more irrational numbers than rational!!

HOW Can that be?

An infinite bigger than another?

But it's true.

>>5686708
>However, adding 1 on the right always gives a larger ordinal number.
>larger ordinal number
That's a contradiction in terms, the phrase you want is "next ordinal number".

ITT people don't know what infinity means

>>5684270
>Right, so, numbers. You interpret 3 as meaning "third", in other words it represents something followed by something else followed by something else. Roughly in abstract symbols,
>A < B < C.

That's where you lost me, OP

Faggot

>>5685353
You can have a line of length pi, though.

>>5686755
What?
'Larger' is perfectly synonymous with 'next' when talking about order.

>>5686755
My phrasing was a bit vague; thanks for pointing that out. What I meant was "larger with respect to the order relation on ordinal numbers", not "larger with respect to cardinality".

lim x-->\infty (x^2)=\infty

lim x-->\infty (x)=\infty

[lim x-->\infty (x)]+1 < lim x-->\infty (x^2)

\infty +1 < \infty

lel guys look what I proofed

OP is rigth. If you disagree, then learn some infinite sucessions. There are some infinites bigger than other infinites.

However, OP: I would recommend to polish your statements. But nice logic is nice.