Friendly reminder that .9999999... = 1 and if you think otherwise you're a fucking retard.
At what point does .9999999 become one?
It doesn't, or else it would've been 1. Unless you're saying that it's so close to 1 that it might as well be 1, and calling it .99999999999999..... is extremely redundant.
>>27469148
IT'S NOT 1 YOU FOCKING NORMIE SCUM
>>27469148
>he doesn't accept hyperreal numbers
incorrecto
>>27469211
1/3 = .333333...
1/3 x 3 = 1
.333333... x 3 = .999999...
We know that 1/3 = .33333333333...
We also know that (1/3)*3 = 1
So (.3333333333...)*3 = ???
0.99999 = 1
-0.99999 = 1-0.99999
0 = 0.00001
0 * (infinity) = 0.00001 * (infinity)
0 = infinity
>>27469373
nigga u dumb af
>>27469321
Nice. I think this has something to do with base 10 number system rather than math itself.
>>27469281
I'm curious. Do other number systems have a way around this problem. What about number systems from Asian countries
0.9999...=1
let's call 0.9999... x
x=1
10x=10
10x should be 9.9999... since multiplying by ten only moves the decimal point one place
10x-9=10-9
9.99999...-9=10-9
0.99999...=1
prove this wrong fags
>infinitesimals don't exist
I'm pretty sure defining .9 repeating as 1 is due to the difference between them being so utterly and unimaginably tiny that it literally affects nothing that doesn't deal directly with infinitesimals in the first place.
Then again, I'm pretty much a math illiterate.
>>27469510
>>27469510
>let's call 0.9999... x
>x=1
You fucked up already. You changed x.
>>27469373
>0 * (infinity) = 0.00001 * (infinity)
>0 = infinity
No, if 0 equaled 0.00001, then 0 * (infinity) would equal 0 * (infinity) in this equation
>>27469510
>this arbitrarily defined variable that just happens to prove my equation helps prove my equation because it proves my equation
>>27469373
0 and infinity come full circle. Numbers aren't linear. There isn't a number line. It's a number ring.
Negative infinity = positive infinity
>>27469536
The way mathematicians define the real numbers there is no infinitesimals*. It's literally just semantic and a consequence of the decimal number system.
How do we define an infinite decimal expansion? We define it as a geometric series. 0.9999...=9/10+9/100+9/1000+...., which can easily be shown to be 1.
*this isn't necessary for 0.999...=1 to be true, alternative number systems can show the same result
>>27469510
You used the conclusion of your proof as a supposition. The reasoning is circular and therefore logically incorrect.
0.999... = 1 nonetheless.
>>27469148
>Friendly
>otherwise you're a fucking retard.
wew lad
>>27469684
This post is nonsense and misuses a slew of mathematical terms.
>>27469148
Just geometric progression my shit up
>>27469785
No it isn't.
Positive and negative infinity are the same thing mathematically. It's just Infinity and it is a hypothetical medium to both positive and negative sides of the number spectrum
Every serious mathematician understands that the number spectrum is non linear
Much like the autism spectrum that you are currently on
Alright fuckers, take it from someone with a degree in mathematics. I doubt a formal proof would convince many of you autists, but here's one anyway.
Two numbers a and b in the real numbers are equal if their difference is 0 (duh).
Equivalently, if for every positive s you can show a-b <s and that a-b>=0, then a-b=0 (you can convince yourself of this).
So here's the proof that 1=.99999.....
Let us denote x=.999...
Let s > 0 (may as well assume s < 1 since 1-x is certainly less than 1)
So s=.a_1 a_2 a_3... where (a_n) is some sequence of whole numbers (for example s=.4322... so a_1=4, a_2=3, etc.)
Let a_k be the first nonzero term in this sequence. So s=.0000000... a_k a_k+1 a_k+2...
Specifically, the decimal representation of s has k-1 many zeros.
Since a_k is non zero and a natural number it must be the case that a_k>=1
Now x=.9999... (that is, infinitely many 9's).
Let x_{k+1}=.999999999...999 (k+1 many 9's)
Obviously x>x_{k+1}
So 1-x < 1-x_{k+1}
Specifically, 1-x_{k+1}=.00000000...01 (k many 0's, you can do this math yourself on a calculator).
Then 1-x < 1-x_{k+1} < s
The first inequality is obvious, the second is since there are more zeros after the decimal in the middle term than in s, it must be smaller (easy mode math).
Hence 1-x < s
s > 0 was abitrary
So 1-x=0
QED
>>27469281
But dumbo, 1/3 isn't equal 0.333...N, it's nearly 0.333...N.
>>27469858
+/- infinity are only the same when you consider the one point compactification of the real number line. An introductory course to topology reveals this.
Furthermore, there are several different types of infinity (countable and uncountable to name two, hell just wiki cardinal arithmetic and you'll get infinitely many types of infinity).
>>27469148
But that's objectively false
>>27469510
Faggot
x = 0.9...
10x = 9.9...
9x = 9.9...- 0.9... = 9
9x = 9
x = 1
>>27469899
Checkmate, atheists :^)
Oregano
.9999999^abritrarily large number = .000001
.9999999^inf approaches 0
memes desui know it doesn't work that way
Python 3.4.3 (default, Mar 18 2016, 17:16:24)
[GCC 4.9.3] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> if 0.999999 == 1:
... print("True")
... else:
... print("False")
...
False
This program would never print True no matter how many 9's I added to the 0.999999
>>27470186
>This program would never print True no matter how many 9's I added to the 0.999999
That's because you're asking it to compare a finite amount 9s to 1. If you ask it to compare an infinite amount of 9s to 1 the program would never end.
>>27469899
Thanks, dude. Clear and concise.
>>27470223
>If you ask it to compare an infinite amount of 9s to 1 the program would never end.
Yeah I tried creating an infinite loop where it would continually increase the 9s, but I'm too dumb to figure out how to do that pragmatically.
The program would never end, but it would also never even theoretically be equal to 1 no matter if it ran for an infinite amount of time.
>>27470186
Nigga how fucking retarded are you??
Real numbers are equivalence classes of Cauchy sequences.
[.9,.99,.999,...] ~ [1,1,1,1,1,1,1,1...]
>>27469421
What the fuck do you think Asians use? Base 11? Get the fuck out of here you retard.
>>27470582
You're right I am retarded.
What the fuck is this shit? If you're so smart explain this.
>>27469148
ITT: people who don't know what an approximation and the squiggly equal sign is
>>27469373
>-0.99999 = 1-0.99999
But that's wrong.
>0 = 0.00001 because I say so
>>27469148
1/3 or 0.3333333 recurring does not actually represent an infinite number of decimal threes, but rather a number that can't be represented with numbers that if multiplied by 3 would equal one.
0.333333 is the closest we can get to representing 1/3 with decimal numbers.
>>27469211
0.9999... isn't a REAL number so to express it as a real number it is 1
>>27470793
see:
>>27471108
same goes for 0.99999999999999 recurring
I just don't get it. Is .0000001 not a number? It's still something...
>>27469148
If I'm 0.999999 of the way towards a vagina with my dick, but technically an infinitely small amount away from being in it... Am I a virgin or not?
>>27471225
It's not 0.0000001, it's 0.000...1
Big difference
>>27471225
that doesn't exiist.
>>27471108
What?
1/3 = 0.3333.... exactly (note the ...). It's well-defined, it's the number which is the limit of the sequence 0.3, 0.33, 0.333, ....
>>27471145
0.999... is a real number (it is on the real line). It is another decimal representation of the real number represented by 1. Decimal representations are just not unique (which is obvious 0.9999....=1=1.0=1.00=1.000...)
Anyone who says it doesnt equal 1 either doesn't know shit about how periodic numbers work or is baiting.
This is a fact.
ITT: A bunch of fucking idiots that never went to college and LITERALLY proved that .9999 to infinity IS EXACTLY 1 with geometric series.
>Save the planet and kill yourselves if you think otherwise.
>>27471337
0.333... =/= 0.333 (going on for ever)
If
0.333... = 0.333, then
1/3 = 0.333
1/3 * 3 = 0.999
however
1 != 0.999
We don't say 0.999... = 1 because it's an approximation, we call it one because it actually does equal 1 as in, to an infinite number of decimal places.
The ... notation tells us that it is a recurring number. A recurring number can only be represented accurately by fractions, all decimal attempts to represent it are approximations unless they use the ... notation.
1/3 != 0.33333333333 (going on for ever)
0.333... != 0.333333333 (going on for ever)
