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/sci/ - Science & Math

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9958751 No.9958751 [Reply] [Original]

If you multiply 0.99999... by infinity you'll never get 100000... but 999999....
And if you don't believe in infinite numbers then you shouldn't believe in infinite numbers behind the decimal point as well.

>> No.9958769

>>9958751
100000....... is equal to 99999........
they're both infinite

>> No.9958795
File: 5 KB, 250x174, q5OL30E.jpg [View same] [iqdb] [saucenao] [google]
9958795

>>9958769

>> No.9958796

>>9958751
I believe in infinite numbers because, unlike retards like yourself, I understand infinity.

>> No.9958802

>>9958769
Those are different infinities you fucktard

>> No.9958808

>>9958802
Prove it

>> No.9958813

>>9958808
Believe what you will, its not my obligation to disprove or teach you anything.

>> No.9958815

>>9958808
>>9958808
Also you are the one that is making the original claim that 10000.... is equal to 0.9999...., you prove it first and then its my turn to get up on the board.

>> No.9958835

>>9958813
>i have no argument

>> No.9958839

>>9958835
Right back at ya m8

>> No.9958850

>>9958815
[eqn]\sum_{n=1}^\infty \frac{9}{10^n}=9 \cdot \frac{\frac{1}{10}}{1-\frac{1}{10}}=1[/eqn]

>> No.9958852
File: 19 KB, 474x266, proxy.duckduckgo.com.jpg [View same] [iqdb] [saucenao] [google]
9958852

>>9958850
[eqn]\sum_{n=1}^\infty \frac{9}{10^n}=9 \cdot \frac{\frac{1}{10}}{1-\frac{1}{10}}=1[/eqn]

>> No.9958859

>>9958751
You don't have to believe in infinity.
You can simply understand the difference between surreal numbers and real numbers. Once you learn how to properly describe surreals, you will be able to use all kinds of 0.999... numbers and operate on them.

>> No.9958870

>>9958859
You better start believing in infinity anon, you are in one.

>> No.9958899

>>9958815
1/3 = 0.3333....

1/3 + 1/3 + 1/3 = 1

0.33... + 0.33... + 0.33... = 0.99... = 1

>> No.9958906

>>9958899
Nooo, 0.33... + 0.33... + 0.33... = 0.99... which equals to 0.99... not 1

>> No.9958924

>>9958906
>0.99... not 1
0.9... - 1 = 0

>> No.9958930

>>9958924
>>9958924
No just no

>> No.9958935

>>9958930
>i have no argument

>> No.9958938

>>9958935
>Unicorns exist

No just no

>You have no arguement

Thats you

>> No.9958941

>>9958938
https://www.wolframalpha.com/input/?i=(0.9...)-1

>> No.9958944

>>9958935
0.99... - 1 = -0.000000...1

>> No.9958946

>>9958941
Appeal to authority is supposed to convince me somehow? 0.999...=1 is an approximation nothing more nothing less, there is infinity between those two numbers.

>> No.9958947

>>9958941
Im acctually blowminded, just found that thread and is acc super intersting, have you got any proof to show that ? :)
Cause Im guinuenly interested in seeing how it works out
(Being serious rn)

>> No.9958950

-0.000000...1 = -0.0... = -0 = 0

>> No.9958954

>>9958946
>is an approximation
prove it

>> No.9958956

>>9958950
The fuck you saying mate ? That’s just not true unless you accuretly precise the number of s.f. you want...

>> No.9958959

>>9958947
\\ 0 < p < 1
\\
1 = p + (1-p) ~~~~~~\overset{1}{\overbrace{[=====p=====|==(1-p)==]}} \\
= p[x+(1-x)] + (1-p) ~~~~~~\overset{1}{\overbrace{\underset{p}{[\underbrace{=====x=====|==(p-x)==}]} ~~ + ~~ (1-p)}} \\
\\
\dfrac{x}{p-x}=\dfrac{p}{1-p} \Rightarrow x- xp = p^2 - xp \Rightarrow \underline{x=p^2} \Rightarrow \underline{(p-x)=p(1-p)}\\
\overset{1}{\overbrace{\underset{p}{[\underbrace{=====p^2=====|==p(1-p)==}]} ~~ + ~~ (1-p)}} \\
\\
\overset{1}{\overbrace{\underset{p^2}{[\underbrace{=====p^3=====|==p^2(1-p)==}]} ~~+ p(1-p)+(1-p)}} \\
\overset{1}{\overbrace{\underset{p^3}{[\underbrace{=====p^4=====|==p^3(1-p)==}]} ~~+ p^2(1-p)+p(1-p)+(1-p)}} \\
(1-p)+p(1-p)+p^2(1-p)+p^3(1-p)+\cdots =1 \\
1+p+p^2+p^3+\cdots =\dfrac{1}{1-p}

>> No.9958960

>>9958769
1000000.... is provably aleph1, whereas 999999.... is aleph0, so they’re not actually the same size

>> No.9958963

>>9958954
The absolute density of some people, you claim that it isnt and thats the same number, you have the burden of proof.

>> No.9958970

>>9958959
Bro, you’re sayin that:
1 = p + (1-p)
=> 1 = (p+1)+(p-p)
=> 1 = p+1
Which just isn’t true

>> No.9958971

>>9958963
>burden of proof.
>>9958941

>> No.9958972

>>9958971
A link isnt proof

>> No.9958975

>>9958970
EDIT: It’s not true for every integer

>> No.9958976

>>9958970
>1 = p + (1-p)
= p+1-p = 1

>american education, folks

>> No.9958980

>>9958972
your bs is worthless

>> No.9958981

>>9958976
How are you just getting rid of the brackets like dat ? xD

>> No.9958985

>>9958980
Just use logic for once will you?

>> No.9958986

>>9958981
>american education, folks
does mommy tie your shoelaces for you?
your lack of any higher mental functions is obvious

>> No.9958991

>>9958985
nah, you show your links first

>> No.9958997

>>9958991
I dont have links, i am just conversing based on logic not even mathematics.

>> No.9959004

>>9958986
Instead of trying to seem or look smart when ur just an asshole, could u just explain how you’ve come to this conclusopn and eventually show your working just like a real smart guy would ?

Cause you’re the one showing a lack of mental functions rn

Mistakes can be made and even if this dude made one, at least he showed and he came to his conclusion

>> No.9959013

>>9958802
no they're not, they're both aleph_0

cantor yourselves dumbasses

>> No.9959014

>>9959013
How are the same thing? At what point does 0.999 becomes 1? Honest question.

>> No.9959031

>>9958997
kek, a classic fapmaster surfing from mom's basement

>> No.9959032

>>9959014
well they’re both not well defined representations of infinity, since the notation is not real math notation, but if you count all natural numbers (as opposed to real numbers) they have cardinality aleph zero

so if you represent the “infinity” of natural numbers (integers) as 999... or 888... then i guess you mean “make a natural number bigger than all the rest” and there are only aleph zero natural numbers, so whatever natural number version of infinity you come up with must be aleph zero

>> No.9959034

>>9959004
>he came in his sock at best

>> No.9959039
File: 3 KB, 635x223, r8.png [View same] [iqdb] [saucenao] [google]
9959039

>>9959032
muddled thinking
inf is larger than any real number
it isn't "a number made bigger"
inf isn't a number, it is separate from R

>> No.9959043

>>9959032
Ok imagine a graph, make one line (a) starting from 0.999 of the y axis and another (b) starting at 1, extend them to infinity, at what point in the x axis will that lines meet? No matter how close you take the (a) line it will never reach and touch (b) will it?

>> No.9959048

>>9959034
Fuck off m8

I believe we need smart people on Earth, but I also believe they shouldn’t be fags like ya

>> No.9959049

>>9959043
they meet at infinity, wouldn't call it a 'point' tho

>> No.9959052

>>9959049
How can they meet at infinity? How can they even touch since you can always just keep dragging them along in a completely flat plane?

>> No.9959054
File: 118 KB, 960x720, snowman_back.jpg [View same] [iqdb] [saucenao] [google]
9959054

>>9959048
awww the snowflake melted

>> No.9959059

>>9959039
of course it's muddled thinking because the notation is nonsense: 999... is not real notation.

anyhow you're talking about real numbers, but i'm talking about natural numbers. keep in mind that the cardinality of the real numbers is larger than that of the natural numbers (c is larger than aleph_zero)

>> No.9959061

>>9959052
>>9959039

>> No.9959064

>>9959061
Infinity is a concept so what? How does that answer my question? Care to elaborate a bit on it?

>> No.9959066

>>9959059
just keep separate
the members of a set
from
the amount of members in the set

>> No.9959073

>>9959064
the lines never meet in R, they only approach each other
for the lines to meet, they have to go to infinity

>> No.9959080

>>9959073
So the lines never meet right? Thefore 0.999... can never be 1

>> No.9959085

>>9958960
No.

>> No.9959086

>>9959080
the definition of a real number is that
the lim as x-->inf *IS* the value

so 0.9... = 1

>> No.9959092

>>9959086
You lost me, laymans terms maybe?

>> No.9959100

>>9959066
yes, true. aleph_zero is not in the natural numbers, so fine. and neither is "infinity"

but if somebody writes down 999... or 1000..., then what that means to me is "infinity" and it also means they're writing integers

aleph_zero is the cardinality of the natural numbers, and the only thing i can equate "999..." with is the same thing as aleph_zero

anyhow that's just my interpretation of meaningless notation. but it's pointless to argue this really without real notation. it's like asking whether 9.10.9 is greater or less than 9.9.9

>> No.9959101

>>9959039
Infinity is not larger than any real number because it's not a number.
ω is the smallest number larger than any real number.

>> No.9959109

>>9959092
mathematicians use infinity in practise, if not literally
instead of using infinity directly, they (and we) set us this fancy lim process where x approaches inf but never actually is inf, in other words x stays within R
then they use the lim result to be the same as if inf would have been directly used
thus getting the benefits of inf (and there are a shitload of those, it just werks) while managing to keep x within R in the analytic inspection.

>> No.9959112

>>9958796
You don't, you just know how to use math to represent it

>> No.9959113

>>9959100
Alpeh_zero is a cardinal, not ordinal number. It's supposed to represent cardinality of a sets.
I suppose ordinals like ω should be used in context of ordering numbers.

>> No.9959115

>>9959109
So its a logic excercise that you use to produce 0.999..=1 not an algebric one, in other words it tends to infinity but never reaches it but we say we do just so we can shitpost in journals and online boards.

>> No.9959119

>>9959101
>>9959113
fine, i admit it, i'm a physics person
i never covered ordinal numbers in my math double-major, so yeah, omega, sure, this must be the answer

but there doesn't seem to be a coherent answer given here in terms of ordinal numbers. well, not an answer, but an explanation of the concept (since the question uses nonsense notation)

>> No.9959121

>>9959115
the algebraic one exists for geometric series, since that is unusually simple

see >>9958959

>> No.9959126

>>9959121
Yeah i dont understand that, i am not in a STEM field that looks gibberish to me, i am only going based on reason and what geometry i remember from school(thats why i gave the xy axis example) how does 0.999..=1 translates in geometry exactly?

>> No.9959136

>>9959126
funny, that proof is very geometric, just cutting up the number 1 in pieces in a systematic way.

since all you are doing is cutting up, it is always guaranteed that the total sum is 1

>> No.9959143

>>9959136
Present to me an example of that geometric cutting if you will?

>> No.9959147

>>9959143
https://en.wikipedia.org/wiki/Geometric_series

>> No.9959149

>>9959147
Again with the wikipedia links.......
How any of the information on that page prove 0.999...=1?

>> No.9959157

>>9959149
>First topic in "applications"
You are a genuine retard

>> No.9959159

>>9959157
What makes you think i can understand what it says there, i see only brakets and such, it looks more like computer code.

>> No.9959166

>>9959159
>Turn off adblocker
>Turn on JavaScript
Do you need help affixing your shoes to your feet as well?

>> No.9959175

>>9959166
Well having some help when starting on a new field doesnt hurt now does it?

>> No.9959234
File: 3 KB, 240x160, DoubleIanKnot1.gif [View same] [iqdb] [saucenao] [google]
9959234

>>9959175
>Well having some help when starting on a new field doesnt hurt now does it?
Certainly not.

Now your shoes have likely come pre-laced so I won't waste time there. Now, the general idea is that you need some way of tightening and then securing the opposite sides of the shoe to prevent it from coming loose.

Begin by crossing the laces and pulling them tight, then, while keeping tension on each of the laces, form a loop on each side and pull them through each other as in the diagram. This process can be remembered using the mnemonic device of:

>Loop
>Swoop
>Pull

The knot can be untied by pulling on the free end of either shoe lace. I hope that clears up any confusion you had on the issue.

>> No.9959239

>>9959234
Thanks anon, it was really eye opening.

>> No.9959257
File: 152 KB, 568x433, amien gril.jpg [View same] [iqdb] [saucenao] [google]
9959257

>>9958751
why dont they just say its an approximation rather than pretend they can use infinity in math

>> No.9959286

>>9959257
'cuz it aint

>> No.9959298

>>9959286
where did you hold inifinity?

>> No.9959305

>>9959298
on the top shelf next to the sugar

>> No.9959332

>>9959286
ok so you go to infinity, you should still see .999...
now you want to bring that information back but are limited, so you approximate. its not really 1.

>> No.9959347

What is .000000...1 + .000000...1 x .000000...1?

>> No.9959499

>>9959109
I don't like that 1 / infinity is zero... always bothered me

>> No.9959509

>>9959499
1 / infinity is not zero, division is not defined over infinity
however 1/n gets closer to zero the larger n is so 1/infinity = 0 is true-ish

>> No.9959516

>>9958751
>If you multiply 0.99999... by infinity you'll never get 100000... but 999999....
Where the fuck did you learn math?

>> No.9959542

>>9959112
>Imagine being this autistic.

>> No.9959545
File: 182 KB, 953x613, .9 Repeating = 1.jpg [View same] [iqdb] [saucenao] [google]
9959545

>>9958944
Retard.

>> No.9959554

>>9958946
If it's an approximation, then there's some error. If there's some error, then there's "space" for another number in between .9 repeating and 1. If there's space, then, because the reals are dense, at least one number exists in that "space". Give me that number and PROVE your claims.

>> No.9959565

>>9959149
Hint: you can rewrite .9 repeating as a geometric series.

>> No.9959567

>>9959554
Cant i just keep adding 9s without ever stopping or any other single digit number, when is the point that i will be forced to ass a two digit number so it becomes greater than 0.999....

>> No.9959572

>>9959567
Did you have a stroke in the middle of typing this response?

>> No.9959576

>>9959572
No i dont think so, still havent answered me though, cant i just keep adding digits?

>> No.9959577

>>9959576
To .9 repeating? It already has all the nines, you don't "add" any.

>> No.9959580

>>9959577

So its an infinite series of 9s?

>> No.9959583

>>9959580
Yes. You can rewrite .9 repeating as an infinite geometric series. The you can prove it converges, and converges to 1. Therefore .9 repeating equals 1.

>> No.9959585

>>9959583
Because it converges, and that means approximating if my english is correct, so we say 0.999..=1 it doesnt really.

>> No.9959592

>>9959585
The .99999... literally means the object that series converges to, not the series itself

>> No.9959594

>>9959585
Incorrect. The infinite 9's aren't added, they're already there. So saying that the series 9/(10^n) converges to 1, and that .999...=1 are exactly the same statements.

>> No.9959603

>>9959592
>>9959594

Still i dont understand at what point does 0.9999... become 1. We just say it does, but it really isnt the same number is it?

see that thing i said a while back >>9959043

I am not trying to spite you or anything i genuinely dont get it. All it looks to me is that we found a cool algebric trick to say 0.999..=1, although to a layman (me) they look like totally different numbers.
Ofcourse you can say they converge but you just say they do they dont actually do so, we just cant handle infinity therefore we round it up.

>> No.9959618

>>9959603
Think of it as the decimal equivalent of the statement 9/9=1. "Clearly" those two sides are different. The left side has nines and a fraction, whereas the other side is just a 1!

>> No.9959626

>>9959618
9/9 does equal 1 on that i agree if my school maths dont fail me, but how does that correlate to 0.999... if we made that number into a fraction wouldnt it be something like 8.99.../9?

>> No.9959633

>>9959626
1/9=0.1...
9*1/9=0.9...

>> No.9959637

>>9959626
I literally told you how it correlates. It was meant to show you that the same number can have different representations.

Another example:
1/9=.1 repeating.
2/9=.2 repeating.
.
.
.
9/9=.9 repeating=1

>> No.9959639

>>9958751
Can we ban all the bait about .999... and just have a sticky or bait for meme tier "discussions"

>> No.9959641

>>9959633
>>9959637

I just cant imagine it on a graph i can imagine two parallel lines that can get extremely close to each other(approximating) but never converge until someone(an observer) says they do just cause, isnt that what euclid was raving about in his 5th postulate? Completely flat plane parallel lines on 90 degrees never converge.

Also why is 1/9=0.1 isnt 1/10 supposed to equal 0.1 ?

>> No.9959644

>>9959641
>Also why is 1/9=0.1 isnt 1/10 supposed to equal 0.1 ?
I typed .1 REPEATING, you illiterate fucker. And the ... in the other guys comment means REPEATING, you illiterate fucker.

>> No.9959652

>>9959644
Wow easy there cowboy, no need to get mean, what do you mean by .1 repeating, show it to me as a number, i am neither a mathematician nor is english my primary language. Chillax dude.

>> No.9959657

>>9959652
.1 repeating = .111111...= 1/9
This is literally grade school level stuff.

>> No.9959667

>>9959657
I wasnt paying attention in class dude come on, ok i get the repeating part, care to move on to the next one now?

>> No.9959672

>>9959667
/sci/ is not a classroom. Go read an elementary math textbook and then come back. You need a BASIC understanding of numbers to hope to understand this material.

>> No.9959675

>>9959672
pfff you are no fun