.99999... = 1

.99999... = 1
prove me wrong
you can't

Other urls found in this thread:

en.wikipedia.org/wiki/0.999...
youtu.be/TINfzxSnnIE
twitter.com/NSFWRedditGif

Decimals aren't integers.

1=1

0.9999999999.....*10 = 9.9999999... | 1*10=10
9.99999999 - 0.9999999999 = 9 | 10-1=9
9=9 .: 0.9999999...=1

Wow we already have some retards in the thread.
Okay get ready for me to break your clits.
.999...=x
10x = 9.9999....
10x - x = 9.9999... - .999999
9x = 9
x = 1

Yet rationals have the same cardinality as integers.

Its not the same because its precisely the reciprocal of infinity away from 1

0.999...=1-1/inf

QED

wow you're retarded
decimals are literally anything in base 10

an infinitesimal 1 is uncountable and cannot be subtracted from 1 since there will always be another 0 before it.

Clearly you meant that fractions aren't the same as decimals but didn't have the brain power to find the word. Either way, .9999999... as a fraction is 9/9, and therefore equal to 1.

1/3 does not equal 0.333... that is simply the nearest base10 approximation.

>ITT: simplemath

Then tell me what it means, Newton.

1/3 does equal .333...
Just because a number doesn't have a stopping point doesn't mean it's any less of a number.
>Pi isn't actually 3.1415926... that's just the nearest approximation.
>actual autist

no but my post equals 1 check em

>8
so close

You are looking for a solution that will work in a calculator. There isnt one. But that in itself is not evidence that 0.99... = 1

0.999...=1-1/inf
>prove me wrong

using infinity as a proof of a value isn't possible
since any number added or subtracted from infinity is still infinity
1/inf = 0
>prove me wrong

en.wikipedia.org/wiki/0.999...

this seems right... is it for real or are you fucking around?

1/3 can only be truely represented in a base that is a multiple of 3.

0.33.. approaches 1/3 but never achieves it, by the same margin that 0.99... never hits 1

>en.wikipedia.org/wiki/0.999...
I'm not fucking around. That's one
of the many algebraic proofs.
Refer to the page linked by

No. An approaching number would eventually
end in a zero, thereby making it not equal 1/3.
.333... never has an end

If you agknowledge infinity as a mathematical concept (and you must) then you have to agknowledge the reciprocal of infinity. Which is the gap between 0.99.. and 1

I don't need to prove you wrong.
It's a true fact.

I never believed this approximation until your counter-argument just now.

youtu.be/TINfzxSnnIE

Easiest calculus proof:

.999999... Can be expressed as:

.9 + .09 + .009 +....
OR
9/10 + 9/100 + 9/1000 + .... 9/10^n

Which is the sum from 1 to infinity of 9 *(1/10)^n. Which is a simple geometric series that converges to 1. By the formula A1/(1-r), where A1 is the first term and r is what each term changes by. Plugging in we get:

.9/(1-1/10) = .9/.9 = 1

>high school maths detected

...

basic math skills
not really something I need to learn

I would just go visit s.n,a,p,c,h.a,t,y(,)me to leak school's hottest girl's nudes.

Nope
It keeps adding 1 so that means u get numbers like .9999999999999998 so it can never be equal to 1

wow you're retarded. .9999... means it doesn't round to an 8 like a fucking calculator. Go back to algebra 1.

9(.999) =/= 9

BTFO

9(.999) = 9*(1/9) = 1

BTFO

1/9 =! 0.99..

1/9 = .111...
2/9 = .222...
3/9 = .333...
4/9 = .444...
5/9 = .555...
6/9 = .666...
7/9 = .777...
8/9 = .888...
9/9 = .999... = 1

>9*(1/9)=1
Kek.
1/9=.1111...
1 divided by 9 does not equal .999 you fuckin dolt

goodfellas dog pictured painted by joe pesci's mom in the movie?

9(.999)=8.991
BTFO

retarded as fuck
.999...=x
10x = 9.9999....
10x - x = 9.9999... - .999999
9x = 9

You probably should go to s.n,a.p.c.h.a.t.y(,)me to fap to your ex-gfs nudes.

.9

Nope.

0.33.. only approaches 1/3

It never achieves it.

Same with all fractions from prime bases.

if .99999.... were equal to one then we wouldnt be able to tell them apart

but since we can tell them apart they must be different

QED

You are correct. We have accepted your assertion as asymptotic truth.

thats actually a good argument but QED doesnt make sense at the end of it

you can actually put this into completely grammatical terms and solve the OP's answer without even refering to numbers

if we say "two things must be different in order for us to tell them apart"

and then we say "we can tell these two things apart"

then we can finally say "since we can tell them apart they must be different"

this is a more philosophical, general, and useful version of that post

You mean it uses more words to say the same thing?

no i mean instead of referring to numbers specifically we can use the principle for any idea or object

there's nothing to prove wrong. if you are trying to find proof that you are...learn calculus

Ask yourselves this. If there lies a number in between two other numbers, then there must be some sort of space there to place it. Can you think of a number to place between an infinite amount of .9 and 1.0? No you can't because it doesn't exist. That's the laymans terms for the geometric series proof.

but numbers dont need space because they dont have extension

you could come up with an infinite amount of numbers between two numbers

there are 0 numbers between .9999.... and 1

then why are they different?

they're not

then how do we tell them apart?

> .99999... < 1
True

thats a good one too

you could say something like "any decimal must be smaller than a whole number"

58008

Turn your phone upside down for hilarity

The gap between 0.99.. and 1 can be explicitly described as 1-1/inf

There is a gap, it is just infinitesimally small.

1-1/inf

You're retarded and your bait is shit.

.99999 is .99999
1 is 1
If .99999 is 1 then it would be 1.
If .99999 is 1 Then $999,999 is actually 1 million. And it isnt.

so what?

also look at this thread full of fucking nerds

im over here doing nasty things with nasty sluts and also bankroll coming in and have some good kush too

enjoy doing more math losers

Heres the thing buddy, of course $999,999=$999,999

We're talking about an infinite amount of .9. Its kind of hard to explain without you knowing calculus.

Refer to this for an explanation

1=2
prove me wrong you cant

>tfw math major
literally everyone in this board is dumb af
.9999999... = 1 in some contexts but not others

Usually tho, yeah they're the same number. If you're in the reals then they are equal, and that's usually what people mean. The context of the "=" is what matters.

>.9999999... = 1 in some contexts but not others
In all contexts. Trump University?

>58008

55378008

>tfw this guy doesn't even know you could define an algebraic structure in which infinitesimals are numbers, in which case they are not equal

He is correct

>tfw this guy thinks that construction serves a purpose outside masturbation
Not everything you can define is useful.

Nobody cares.

This construction serves as a counterexample to the statement ".99999.... = 1 in all extension fields of R" so that's as much use as I need familia

...9999 = x
...9999.9 = x/10
-0.9 = 9x/10
-1 = x

...9999 == -1

....999.999... = x
...999.999... = x/10
0 = 9x/10
x = 0

...999.999... = 0

or:

...999.999... = ...999 + 0.999...
...999.999... = -1 + 1
...999.999... = 0

>this guy has never done ring theory

The reason .999.. is said to equal 1 is because of "math patterns"

like

9/1=.1111111...
9/2 = .222...
9/3 = .333....
9/4 = .444...
9/5 = .555...
9/6 = .666...
9/7 = .777...
9/8 = .8888
9/9 "SHOULD EQUAL .9999 RIGHT?? BECAUSE LOOK AT THE PATTERN"

but I say just because you observed a pattern, doesn't mean the pattern has to continue. There is no proof that said pattern continues, and therefore you are wrong. .999... does not equal one.

That's not the reason they're equal lmfao. I'll do a proof for you.

First off, we're in the context of real numbers.

Suppose by contradiction .99999... =/= 1

Thus there exists a nonzero real number x such that x = 1 - 0.99999.....

so x = 1.000000... - 0.99999....
0.0000......1

This is a contradiction because no such real number exists (you cannot have an infinite number of 0s followed by a 1, that's called an infinitesimal and doesn't exist in the real numbers).

0.999 * 10 = 9.99
9.99 - 0.999 = 8.991

Doesn't really matter how many times you push back the decimal point. You're still looking at the same problem.

Infinitely small difference. Just like when we started.

>implying infinity doesnt exist

I disagree.
.0000...1 can exist according to my math.

We are not computing this number, it isn't like "oh the last 1 won't fit because there are an infinite number of 0's before it."

1 + .99999... = 1.99999...
1 + 1 = 2

2 =/= 1.99999

Any fag who thinks otherwise is retarded. 1 is 1, .99999999.... isn't 1.

Bad example lol. But you are right.
.9 repeating is simply that, .9 repeating.
IT is the closest you can get to 1 without it being one.

To many people think like a calculator, and like to "compute" the number .9 repeating, and end up just "rounding it to one"

When if you had infinite time, and infinite paper, you could write .9999999... forever, and not once while you are write it will what you have written equal one.
Even if that infinite process took place in one second, after that once second, I still do not believe you would have succeeded.

Why do all these mathematicians think they can create their own rules for math?
There are no rules, it is pure logic.
you can't just say, "there are no infinitesimals lol" lol u dont make the rules stfu

.999999... =/= 1
.999999... ~ 1