/sci/ - Science & Math

>>11595594
all of these so-called ""infinities"" belong in quotation marks desu

>>11595600
why?

stop making this fucking thread

>>11595627
I'm trying to stop it by summarizing both sides.

>>11595648
>hey lad whachu doing
>ah, I'm just trying to put out this fire by throwing gasoline at it

>>11595667
How does appealing to both sides heat up the discussion

>>11595667
spot on

>>11595594
>”limit infinity”
You need to use the grave key ` to make a opening quote marks in latex

>>11595702
Thanks, but I'm fine with this. My point is clear through the table and unfortunately there isn't really a mathematical term I know for "limit infinity".

>>11595690
I already replied to that dude you idiot, at least answer my question

>>11595712
Absolute infinite, [math] \Omega [/math]

>>11595717
Cardinal infinity - omega - is not the same as limit infinity.

>>11595764
*ordinal infinity - omega, sorry

>>11595594
Yes yes, very well op, very well. HOWEVER. What if I can't read? How can you then show to me that 0.999...=1?

It looks like != came out victorious once again

>>11595594
>doesn't know what a limit is

>>11595770
>>11595764
[math] \Omega [/math] is not ordinal infinity. It is larger than anything. Ordinal infinity is represented by [math] \omega . [/math]

>>11595788
Where did I make an error involving limits?

>>11595787
By telling you.

>>11595675
You couldnt have made this post in the other 8 threads shitting up the catalog?

>>11595787
I guess I have been disproven and must delete the thread now, sorry for being such a brainlet

>>11595791
Sorry, I read that on my phone and mistook it. Can you link me to some article describing it? In which area is it supposedly being used?

>>11595798
I could have, but this way more people see it. Since this post is not a direct reply to anything, its goal is to reach as many people as possible,

>>11595795

>>11595803
https://en.wikipedia.org/wiki/Absolute_Infinite
It's not really properly defined here, but it gets the idea across. I don't know how to define it.

>>11595811
Note the equals sign 4 lines below it, genius.

>>11595811
Holy shit fuck off, what value would you assign to the limit then?

>>11595814
Its existence is literally disproven in there:

"The system Ω of all [ordinal] numbers is an *inconsistent*, absolutely infinite multiplicity."

>>11595808
Like everyone else then. With your logic, why wouldn't all of us always make new threads when posting something which isn't a direct reply to someone else..?

Test

>>11595833
Well as long as it doesn't belong in /mg/, that's what you should do. I really don't see the problem.

>>11595836
Success

>>11595819
A limit is a mathematical concept that explains what it approaches fucktard. Notice all the "approaches"?

>>11595848
Yes, as x approaches infinity, f(x) approaches some value. Thereby we conclude that at infinity, f(infinity) is equal to the limit.

>>11595848
And we say that a limit of a sequence is equal to some number if that sequence approaches the number, you absolute mong.

>>11595827
That just means that it's not well-ordered. It makes no such claim on its existence.

>>11595858
How would it not be well-ordered if it only consists of ordinals, which are very clearly well-ordered?

>>11595862
idk then. I guess there isn't a term for "limit infinity".
I reckon it could make sense in the context of surreal numbers, since they are so different to any usual number system, e.g. they are not a set.

>>11595867
Well I think "limit infinity" is good enough and it describes the concept pretty well.

Also I doubt the surreal numbers are related to this

>>11595854
Yes that's what a limit does it's essentially the same as rounding it wouldn't ever reach 1 even at infinity which is why limits simplified what f(x) actually is down to either converges and diverges.

>>11595876
Well in the surreal numbers, for any ordinal [math] \delta [/math] you can have [math] \delta [/math] many 9's following the decimal point, and that would be less than 0.999... with an absolute infinite (or limit infinity) 9's following the decimal point. The number of 9's following the decimal point is larger than any ordinal.

>>11595882
It is NOT the same as rounding. But it absolutely would reach 1 at infinity.

>>11595882
No that's wrong. Read the definition, and note the equals sign. An equals sign (=) means that the numbers are equal.

>>11595890
That's right

>>11595898
>>11595894
Read the damn definition again "a limit is the value that a function "approaches" as the input "approaches" some value" it never stated that the function will become the value. It's just a way to simplify things.

>>11595917
what's your point ?
tldr; 0.99.. != 1 ?

>>11595594
The only actually useful thread in this cesspool of comparing 0.999... to 1.

>>11595917
The definition also includes the word "is".
It literally says that the limit IS the value that a function or sequence approaches. You wrote it right there.

>>11596060
Thanks mate, that was the intention

>>11595594
Since I learned that 0.999... and 1 aren't actually real numbers but rather representations through a decimal expansion, I have lost the ability really see what the issue is with said representations being noninjective.

>>11596160
>I have lost the ability really see what the issue is with said representations being noninjective.
literally no issue. that's the joke.

>>11596160
You mean where the issue lies with 1 and 0.999... representing the same real number? A lot of people take issue with it, and if you define 0.999... as a transfinite sequence with only [math]\omega[/math] members where each sequence represents one digit, then it actually is different from 1 (in the surreal numbers)

>>11596182
*where each member of the sequence represents one digit (a 9)

>>11596091
I can't tell if you know what the definition is or not.

>>11595594
Infinity's not real.
http://aynrandlexicon.com/lexicon/infinity.html

[eqn]Let \; x=0.999...[/eqn]
[eqn]∴10x=9.999...=(9+0.999...)=(9+x)[/eqn]
[eqn]∴9x=9[/eqn]

>>11596310
Yes, that is a very great argument when talking about an infinite stream of 9's - limit infinity. However it doesn't apply when talking about an ordinal infinity, since it is possible to define a last 9. That's the reason that one is the only one where 0.999... and 1 are not equal.

>>11596267
Retard, infinity is clearly mathematically defined. This is not about the actual universe, just about pure theoretic constructions.

Also good I have my coincidence detector enabled.

>>11595602

because they are hindu shizo concept

>>11596492
Obviously

>>11597883
The whole point of this thread is to have clarity, so please clarify what infinity you mean in your definition of 0.999...

>>11595594
Complex?

>>11596476
>infinity is clearly mathematically defined
That is not true. But give it a shot anyway.

>>11595594
It is ironic, because I just made two small chairs. Let us get together and have a brew and a chat.

>>11598221
The cardinality of a set that is not finite. The axiom of infinity guarantees such a set.

>>11596310
9.99... would have a 0 at the end 9.99..0 therefore you can't subtract the original .999... from it. And yes some infinities can be larger than others.

It can also be seen in .999... + .999... = 1.99..8
We know it will be 8 because the two infinities we're adding are the same size.


.333.. = 1/3 is just something we're made to memorize because it's the only decimal way to represent 1/3 but .333... will never reach the whole 1/3, not after the trillionth decimal point and not at infinity either just like 1/x will never touch the x axis.

>>11598256
I see. That is worse than I thought it would be. Dear anon, no, in mathematics there is no cardinality called "infinity".

>>11595594
Is this true, /0.999.../?

>>11598215
What do you mean "complex"? I never mentioned complex numbers.

>>11598221
https://en.wikipedia.org/wiki/Ordinal_number
https://en.wikipedia.org/wiki/Cardinal_number
https://en.wikipedia.org/wiki/Limit_of_a_function#Infinite_limits

All of these have been VERY rigurously defined and used

>>11598275
He is referring to [math]\aleph_0[/math] and you very well know that. And yes, there is not one infinite cardinality, rather there are infinitely many infinite cardinalities.

>>11598268
If you're talking in the surreal numbers and about the omega'th digit, then yes, you're correct. As I have already stated, his proof doesn't apply in that case.
However when talking about a never-ending stream of 9's or 3's, which is what the notation usually implies, using a limit to derive a value is the correct way to go over it, in which case the value is indeed exactly 1 or 1/3.

>>11598277
Usually 0.999... implies a never-ending stream and thereby the limit case, resulting in 1. So yes, the value would indeed be i.

>>11595811
>>11598326
The very definition of a limit states that the answer to a limit is what the function "approaches" never what the function will actually become.

The core of the problem in the minds of those who believe less than 1 is 1 is this:

Their inability to comprehend that ".999..." isn't the same as "1" is directly tied to their inability to grasp eternity and infinity. Their minds have basically been programmed to believe eternity and infinity are impossibilities. Over the course of many generations of indoctrination into an alien worldview, their parents and their parents etc gradually "learned" to be unable to comprehend it and this "learned disability" was inherited, and encouraged/fueled by various external factors from the echoing modern culture.

So basically, they're mentally damaged.

This difficulty they have with eternity/infinity shows up in many different fields, from math to astrophysics.

This mental handicap is inherited directly from the (((Abrahamic))) religions, more specifically (((Christianity))) for us Westernerns. In it's origin, the inability to understand infinity and eternity is 100% Judaic in thought/philosophy. In contrast, the non-Jewish man; the Pagan man, at least the /European/ Pagan man, never had any problem with infinity and eternity. (((Christianity))) introduced into the minds of people the idea of life and the world/universe being linear, starting from point A and ending at a point B, whereas in the Native European worldview everything is an infinite circle.

That's why many people today can't understand that .999 repeating forever will never reach 1 - they refuse to accept the idea of an infinite/eternal repetition. Saying "it's 1" is their method of escaping from the uncomfortable (and to them insurmountable) challenge which the concept of infinity/eternity is to their Judaically-induced mental disease.

>>11598340
Very related.

>>11598338
At the limit point (infinity in this case) the function becomes the limit.

>>11598344
>function becomes the limit
Show me where that is stated

>>11598340
I know this is copypasta but I'll reply anyway

I'm very much able to concieve an infinite amount of repeating digits that does have an end, it is included in the table - ordinal infinities are used to describe such things, it's just that your notation is very unusual if you mean the case of [math]\omega[/math] 9's.

>>11598347
cmon

>>11598354
Yes the definition of limit means finding what the function "APPROACHES" That is the DEFINITION OF A LIMIT.

>>11598373
Yes, as x approaches p, f(x) approaches L.
And when x is equal to p, f(x) is equal to L.

>>11598376
>And when x is equal to p, f(x) is equal to L.
not necessarily

>>11598386
That's correct, but it's the most intuitive extension of the function you're talking about and should be used when it makes sense and is possible

>>11598376
Look what i'm saying is when you're trying find the point of convergence of a function a limit will give you what it approaches. What it approaches does not mean what the function is or ever will be.

Do you agree that 1/x from 1 to infinity will never touch the x axis?

>>11598402
It will touch the x-axis at the infinite point.

But 0.999 isn't a limit right? It's literally endlessly long, with no concept of "approaching" the value. There is no final digit in 0.999, nor do we ever consider it an ever longer series of nines—it is infinite.

>>11598405
>durr hurr it's infinite I can't see it it MUST mean that it'll touch the x axis
Even the fuckers that made limits stated that a limit is only what it "approaches" while it "approaches" infinity.
They were only made to define the point of convergence.

Why the fuck you it touch ever even after an infinite amount of digits if it can't touch it at 100 1 trillion or n^goool do you seriously think there will ever be a number that'll make that function equal the point of convergence?

>>11598409
Well that's what 0.999... usually implies, a never-ending stream of 9's. And a never-ending stream of 9's can best be modelled by the function f(x) = 1 - (1/10)^x, with x approaching infinity. A number obviously doesn't approach anything, it's the other way around: the function approaches the number. And the value of the limit is 1, so when using the "never-ending" definition, we should use limits and arrive at a value of 1.

>>11598412
Yes, I think that. It's the same thing with approximations of pi. All the approximations are never exactly equal to pi, they are all not irrational. However at the limit point the property suddenly changes, the number is pi itself and it suddenly becomes irrational.

>>11598414
0.999... Is not the limit of a function. It is literally infinite nines. The limit says that for any epsilon there is a number 0.999999999 with FINITE nines less than epsilon away from 1. But 0.999... has an actual infinite amount of nines. Get this limit idea out of your heads

>>11598418
Are you suggesting that we know exactly what pi is?

All i'm saying is that a limit is an attempt to define the undefinable. We know that the function will never touch the convergence point, it doesn't matter if you throw in two or three infinities or infinite infinite in the function. This is why a limit is an approximation as it "approaches" infinity.

>>11598435
With actual infinite, do you mean stuff like [math]\omega[/math] ? Otherwise, I don't know what mathematical concept you're referring to.

Also I don't see how the value of "the function that returns a 0 with n 9's evaluated at n = infinity" is not a valid interpretation of 0.999...

>>11598438
"We know that the function will never touch the convergence point"
Why?

Also "approximation" is just blatantly wrong vocabulary, please use "approaching"

>>11598459
How do finitists write down the decimal expansion expansion of 1/9 anyway?

>>11598462
You know exactly what i'm saying and I don't think I have to explain any further. Look at the definition of a limit yourself and derive your own conclusions.

>>11598459
I mean the nines actually go on forever. Tom much for your baby finitist brain?

I solved it.

>>11598581
What infinity is that? Last time I've seen it it was defined as the limit as x goes to +0 of 1/x. If we apply that definition here, we get 1/(1/0), therefore 0. Stop being insane.

If you actually were to use this, at least write [math]1 - (1/10)^\infty[/math]. And since this is defined using the limit, its equal to 1.

>>11598478
>>11598527
What's a finitist? The name could go both ways.

>>11598527
Ah, so you actually mean a never-ending stream. In that case, one should apply the limit definition which was just what I proposed - "the function that returns a 0 with n 9's evaluated at n = infinity"

By definition
[math]0.9999999....=\sum_{n=1}^\infty\frac{9}{10^n}[/math]
and using the equation for the Geometric Series
https://www.youtube.com/watch?v=cD0QoPYc_LI&feature=emb_title
we get
[math]0.999999....=0.9\frac{1}{1-0.1}=0.9\frac{1}{0.9}=1[/math]

>Noticing [math]\frac{1}{10}=0.1[/math]
>mfw discover power series

>>11598702
I'm not calling you a finitist, or anyone else, for the record. But if we must avoid the concept of "actual infinity" we should make sure if this is really possible. Either one must reject infinite decimal expansions wholesale, or concede that 0.999... = 1.

>>11598729
Thanks anon

>>11598750
Well we must reject absolute infinity, but for example using surreal numbers, infinite decimal expansions with 0.999...9 not equal to 1 are possible.

>>11598860
>0.999...9
is this the same as 0.999... ?

>>11598888
No. The notation is a bit weird, but the point is that the number is denoted by a transfinite sequence, which has 9's up to the [math]\omega[/math]'th place, but no more after that. 0.999... normally denotes simply the limit, which is 1.

>>11598860
If we reject absolute infinity can we use decimal expansions in the first place? I am not sure what your own thoughts are in this discussion.

>>11598962
I'm OP. My thoughts are expressed in the table on top. And yes, we most certainly are able to use decimal expansions. There are enough replacement concepts for "absolute infinity" which take its role in various fields.

>>11598976
my dad

>>11598340
here's dumb pagan retard again.
here to say, as i do every time i see his stupid theories, that Christianity promotes the infinite. you never die as a christian, you either stay as a soul eternally in a state of burning, or you stay as a soul eternally loving god with great happiness.

Simple
1/3 = 0.3333333...
3*(1/3)=3*0.3333333...=0.9999999...=1

>>11597883
HOLY BASED
saved for later purging of the onetards

auto ban for spam when?

>>11595594
You're a fucking retard. Cardinals ARE ordinals.

>>11596467
>ordinal infinity, since it is possible to define a last 9.
You're also a retard and don't know what you're talking about. There's no maximum ordinal less than omega.

Just SHUT THE FUCK UP if you don't know what you're talking about. It's really simple. Stick to the basics if you're unsure.

>>11597883

>>11600062
Nigger what

>>11600244
Unironically kys, you're literally to stupid to clearly define 0.999... yourselves. We have to do the fucking job for you.

>>11601278
Holy fuck you're actually a moron

Read this for starters https://philosophy.stackexchange.com/questions/6352/what-is-the-difference-between-an-ordinal-number-and-a-cardinal-number

>>11601279
Wait, what's the problem with a transfinite sequence defined by taking the value of 9 for all finite values, but not at omega anymore? Or only one further 9, at the index omega+1, but no more after that?