/sci/ - Science & Math

think far as back as you can... and keep going

>>9854111
Assume that there is a finite amount of numbers.
let F be the final number.
F + 1 > F
Therefor there is no final number, and there is not a finite amount of numbers.

>>9854111
Prove to me the universe is finite

>>9854111
Squares have diagonals.

>>9854111
>prove that infinity exists
who said it did?

>>9854111
Infinity exists only in mathematics. IRL (aka in physics), it's impossible.

>>9854147
wtf

>>9854128
If the position and momentum operators of quantum mechanics had finite dimension, then the uncertainty principle wouldn't hold because Tr(XP - PX) would be 0.

>>9854111
Your request needs context before it's meaningful enough to be answered, 尻の女神.

>>9854154

In physics, when your equations give you infinity as a result, it means that either you are wrong somewhere, or you still don't understand enough the phenomenon.

https://www.wolframalpha.com/input/?i=infinity
An unbounded quantity that is greater than every real number.

>>9854162
Prove to me that different sizes of infinity exist

>>9854111
shitty bait, attempting us to answer the question without defining what your version of "infinity" is

>>9854128
yes, this is valid. infinity is the term used to describe "infinite sets" (sets which are NOT FINITE). all one has to do is prove that there exists a set that isn't finite (in this case, the natural numbers)

>>9854166
[math]\aleph_0[/math]
https://youtu.be/elvOZm0d4H0?t=2m
[math]\aleph_1[/math]
https://youtu.be/elvOZm0d4H0?t=4m

>>9854166
>every integer is not prime
>the set of integers is infinite
>the set of primes is infinite, but only a subset of the set of integers

>>9854170
>all one has to do is prove that there exists a set that isn't finite (in this case, the natural numbers)
First you would have to prove that the "set of natural numbers" is actually a set

>>9854170
There doesns't exist such a thing as infinity in the universe. It's a concept humans want to force.

>>9854195
>There doesns't exist such a thing as infinity in the universe
See >>9854157

See OP here? OP is a bot looking to data mine replies. Don't help him. Do not respond to one-line writing prompts.

>>9854182
nah
2n (0,2,4,...) is a subset of n
but both sets are aleph-null

>>9854220
Does that set include the numbers 1 or 3?

>>9854221
>lets pretend infinite is finite

>>9854226
Why not?

>>9854230
https://youtu.be/i7c2qz7sO0I?t=50s

>>9854183
stolen from wikipedia: In Zermelo–Fraenkel (ZF) set theory, the natural numbers are defined recursively by letting 0 = {} be the empty set and n + 1 = n ∪ {n} for each n. In this way n = {0, 1, ..., n − 1} for each natural number n.

Defined this way, natural numbers form a set by definition.

>>9854249
That's a circular definition because it assumes the axiom of infinity. You can form the natural numbers by using successor functions and whatnot, but you can't show that all natural numbers can be contained in a set without assuming the axiom of infinity.

>>9854183
>have to
Not really, take it as an axiom and build your house of cards from there.
Anyone can then collapse the whole thing by showing [math]\mathbb{N}[/math] isn't a set.

>>9854255
fine, disprove the axiom of infinity then

>>9854259
>take it as an axiom and build your house of cards from there
Sure, I'm just saying that getting an infinite set from a finite set isn't possible without the help of "cheats" like the axiom of infinity. I'm not a finitist btw.

>>9854264
>disprove an axiom
I can't disprove it because ZFC can be shown to be consistent by assuming the existence of inaccessible cardinals, but ZFC without the axiom of infinity can also be shown to be consistent.

>>9854161
Has this been proven?

>>9854133
So?

>>9854128
If there are a finite amount of a numbers, and F is the final number, then you cannot evaluate F+1 dummy

>>9854302
the point is you can't construct a set where there is a final number.

>>9854111
I'm not gonna prove infinity exists but i'd play with you the game where the biggest number provided wins and *you play first*.
Each of us provide one number and if you can use a formula, I can too.

>>9854111
Divide 1 by 0

In physics it doesn't exist, yes. But that's just one landscape

>>9854598
Why not in physics?.. However, it appears that, given the accelerating expansion of the Universe, the Universe will grow larger and larger and colder and colder. All of the luminous objects in the Universe will eventually die out, and the Universe will eventually end in a "Big Freeze," where it will be too cold to support any life.
Also there's evidence about singularities in which space-time is bend the singularities when the event horizon are exposed their density approach to infinity and collapse. That's how the Big Bang began.

>>9854605
>>9854605
>Oh, and by chance you don't understand, this rapid expansion given by dark energy began at the big bang for millions or billions of years and still going up.

>>9854111
How do I prove to infinity that it exists?

>>9854111
Also, you can tell that Motion means Infinity, in the universe there will always be motion (movement, events, collisions) so yes there's infinity.

How many points are in a line?
It's infinity.

>>9854170
>this is valid
That is not a valid argument, It is just a existence statement.
given any finite number of numbers, there "exists" another number.
potential infinity is unintuitively, but surely, can be done finitely with no exception.

>>9854111
You in one place and not in another. Infinity is a possible state representation within a selected domain.

>>9854302
then which is the final number smartass?

If You Believe In God, You Have To Believe In The Devil.
If 0 exists, infinity must also exist.

>>9854605
https://www.quantamagazine.org/mathematicians-disprove-conjecture-made-to-save-black-holes-20180517/
What this does show, however, is that infinity can exist "outside" of physics

>>9854768
Zero does not exist anywhere. Infinity potentially exists "outside" of physics.
Here is why zero cannot exist anywhere:
https://plato.stanford.edu/entries/nothingness/

>>9854805
Also, this can never be proven and will forever remain speculation
>inb4 then it's wrong
not rly

>>9854111
infinity exists, like santa claus exists. The question you should be asking is "is infinity physically real", but ill go.ahead and answer. Infinity does exist, mathematically and theoretically. Infinity and an application to that topic i would assume could deal with the expansion acceleration or time of the universe, is that real? Well us in this thread might not know. Thats something that obviously takes time so id say for now, no it isnt real.

>>9854111
n+1...
qed infinity exists mathematically

You are all brilliant scientists

>>9854128
This does not mean that an infinite or infinite'th number exists, though. The merit of the infinity-loop sign has no value to mathematics.

>>9855568
Take for example the description of an infinitely repeating decimal, such as the decimal representation of 1÷3 = 0.333...

Because there is no infinite number, it cannot be said that there are infinite 3's in the decimal. We can analytically extend the work of 1÷3 from
0.3
0.33
0.333
0.3333
0.33333
To
0.3...
but this cheats understanding. Without the notation, everyone would be well enough rationalizing that you can never write enough 3's because the solution of 1÷3 in decimal doesn't play nicely with base-10. However because of the notation of the ellipses or overline, people assume to account for all of the 3's instantly and inclusively, overlooking the issue of inaccuracy by the solution in base-10.

it is true that [math]\frac{3}{3} = 1 \text{ and } \frac{1}{3} × 3 = 1[/math], yet is untrue that [math]\frac{1}{3} = 0.\bar{3} \text{ or } 0.\bar{3} × 3 = 1[/math]

Shits gay brah

>>9854285
If irrational numbers exist, infinity exists.

Try to count numbers until the end of the numbers, and gg if you succes. Because there is no end of the numbers

>>9855596
1/3 = 3/10 + 1/30
= 0.3 + 1/30
= 0.33 + 1/300
= 0.333 + 1/3000
:
= 0.3... + 1/inf
= 0.3... + 0
= 0.3...

>>9854111
Infinity is the name of a symbol that is used in various roles in mathematics, often, but not always, to indicate a limit operation.
It looks like an 8 on its side, and it is found in many texts, so in particular it exists.

>>9854607
That is not quite accurate. For a long time the expansion held back due to a larger density of matter in the universe causing enough gravitational attraction to keep stuff together. It only picked up serious enough acceleration a few billion years ago to ensure that everything will not crunch back to a point again.

>>9855618
Infinity is not a number. 1/inf is as valid a statement as 1/tuna salad

>>9854162
The Wolfram quote is someone's laughable misunderstanding of mathematics. No more no less.

>>9854166
Noice question.
Let R be the set of real numbers.
If oo and -oo are two sets, called infinity and minus infinity, respectively, that are not real numbers, then RU{oo,-oo} is called an "extended set of real numbers", if the ordering and arithmetic of R is extended naturally to this larger set. It kills a lot of nice properties that R has, but who cares.
Now take
Example 1: oo={0} (which is allowed, since {0} is not a real number), and -oo=R. In this case oo has size (cardinality) equal to 1.
Example 2: oo={0,1} and -oo=R. In this case oo has size 2.
This is proof that there exist infinities of different sizes.

z_(n+1)=z_n^2+C

>>9855683
>shitposter vs WA
top kek

>>9855676
no one claims it's a number
'unbounded' is enough to reduce 1/inf to zero

>>9855704
Noice

>>9854805
how many californium atoms do I have on my hand then smartass?

>>9854111
how many natural/integer/rational numbers are there?
how many real numbers are there?
for how far do the pi digits go?

>>9855767
>how many natural/integer/rational numbers are there?
aleph-0

>how many real numbers are there?
aleph-1

>for how far do the pi digits go?
aleph-0

>>9855821
infinities.

>>9855821
>how many real numbers are there
it's only aleph1 if you assume CH. Otherwise it's |R| >= 2^aleph0

>>9854111
count to the highest number

>>9855715
Wolfram has already observed your misguidedness, they are changing the page as we speak.

>>9854111
God exist. God's power is without limits. Therefore infinite.

>>9856351
seek help

>>9856404
God helps

>>9854111
Mathematical concepts aren't objects, they don't "exist".

>>9855717
>1/NaN = 0

>>9857533
blunt math, but valid

>>9854276
check the whole mess related to renormalization in QFT

P1: Infinity = God
P2: God exists
C: Therefore, infinity exists.

>>9854309
*with a successor axiom

>>9855676
You could easily define inf to be the number such that 1/inf = 0 are you such a brainlet that you can't handle a fucking dictionary?

>>9857740
infinity or whatsoever physics and math laws in this world are god's creation. although god has infinite resources in this world, the self sufficient god CANNOT be the infinity. how can the owner of infinity become infinity itself?

>>9857772
>god has infinite resources
he can barely burn patterns on toast these days

what's 1 divided by 3?

>>9859042
Finite

∞

>>9857758
>1/x = 0
>x must exist
may as well say there must be a whole integer square root of 2. You can make up dumb rules all you want, but it doesn't mean they're useful.

This image pretty much summarizes how higher-math brainlets approach the concept of infinity.

Infinity has no real role or value in relation to math or even numbers, but the more 'educated' these desperate brainlets become, the more they start misusing and abusing infinity to virtually mean just about whatever the fuck they want it to mean. They'll say a contained infinite value can exist, and that there are different ordered magnitudes of infinity. Just total brainlet fantasy bullshit, much like Toy Story, and even more specifically much like Buzz Lightyear who is literally a delusional character in the movie.

>>9859064
how many threes are there in that digit in decimal counting?

Infinity MUST exist, but it exists as a property of existence itself. For example, numbers require the property of infinity to exist, they are infinitely separated, and infinitely connected. They cannot work and exist as they do without infinity existing.

>>9860319
you are a fucking idiot. How about you read about set theory you miserable fucking tard

>>9860487
think about it
inorder to there be salt on the table there must be a table
in order to there be a table there must be a floor
in order to there be a floor there must be Earth
in order to there be Earth there must be space-time
ad infinitum

>>9860487
Fuck set theory, that's designed to make cucks like you separate objects when you should be joining them together you fucking idiots. Completely backwards mathematical philosophy.

Infinity and infinitesmals are not real, they are concepts. They express values that can not be expressed using real numbers.

Infinity expresses a value too large to be within the real numbers. Infinitesmals are values too small to be expressed by a real number within the real numbers domain.

>>9854111
Easy, there are an infinite amount of numbers between 1 and 2. 1.1, 1.2, 1.3 etc. Think you’re done? Add another zero after the decimal. Infinite, bitch.

>>9860502
>Infinity expresses a value too large to be within the real numbers. Infinitesmals are values too small to be expressed by a real number within the real numbers domain.

False, infinity doesn't express a value too large, infinity is the expression of infinity, numbers are direct proof of infinity existing as a property of numbers, numbers do not have any beginning or end, only arbitrary ones.

There is no value too large or too small for "real numbers", only the capacity to display such a value all at once.

so either infinite doesn't exist, or numbers aren't closed under addition?

>>9860534
Infinity is not a number, it is a property.

>>9860545
that's like saying a limit is a property and not a number

>>9860545
>>9854162

>>9854598
aren't fields in physics infinite?