Discuss

Discuss.

Well they look different Innit so how could they be the same

Well, 0,5 and ½ look different as well

You and op look different yet you are both faggots

0.333333333333333333 = 1/3 |*3
3*0.3333333333333333 = 3* 1/3
0.9999999999999999 = 1

Let x = 0.999999...
Therefore 10x = 9.9999...
10x-x = 9.9999... - 0.9999...
9x = 9
x = 1

0.99999999....9...
Constantly approaches 1.0 but will never be 1.0

However, for just about every single application, 0.999999...9... = 1

Damn this guy gets it

No, you're retarded.

Exactly.

Don't argue with the proofee, argue with the proof. I don't think it's 1 either, but you can still do a proof.

Of course the problem is it's a proof that, like many others, implicitly relies on infinity being a number when it's not.

Not this again.

>You have 1L of water in a bottle
>You put all the water in 3 cups
>Each cup have 1/3L of water, or 0.333... L
>Now you put back the water in the bottle and it is filled again with 1L of water
>But a cup have 0.333...L of water
>3 cups have 0.999...L of water
>3 cups filled 1L bottle
>1L of water=0.999...L of water
>0.999...=1

This only shows how decimal representations are retarded
In theory they should be adding up to 1, but the structure of a base 10 decimal system cant handle it well.
All this shows is that .3333333333333 while fine in most cases is not a true replacement for 1/3

What is a limit for 200 Alex

Take into fact moisture content in cup after measurements

What happened to the 0.0000000000.....1 drop of water? Evaporated?

Actually, this. Just this.

Decimal system is good enough, but inherently flawed

People like him don't understand the concept of approximation.

0.999... ~= 1 is true.
0.999... = 1 is false.

If there are an infinite quantity of numbers between 0 and 1 then all you are doing is having a schemantic argument about what number you are representing by writing .999999...

There must be a number that is 1-(an infinitely small number less than one) which presumably equals .9999999...

If there does not equal an infinitely small number to create the number that you're representing then you're just representing it badly or lazily.

0.99999999... isn't in fact 1, rounding system fixes it.

...

yeah this guy named wikipedia and google they realllyyy get it

>10x-x = 9.9999... - 0.9999...
But 9.99999999999999 theoretically has infinity-1 9s after it so when you minus .999999999 which has an infinite number of 9s you are actually getting a number that is just smaller than 1 by an infinite amount
.999999999999

Er... sorry, messed that up
9.99999999999999 (10×.99999999)
minus
.999999999999999
Would theoretically equal 8.99999999...1
Same logic though
9.99999(infinity - 1 9s) - .999999(infinity 9s)

Continuing the logic
9x=8.99999999(infinity-1 9s)...1
8.9999999999...1 ÷ 9 =.999999999999
x=0.9999999999

Wow we got the same number we started out with, funny how math makes sense when you do it right

infinity-1 = infinity.

no such thing as infinity

Indistinguishable? Yes
Equal? No

Infinity - 1 is smaller than infinity by an infinitely small amount
Same goes for .99999999... and 1

⅓ = 0.333...
0.333... x 3 = 0.999...
⅓ x 3 = 1
∴ 0.999... = 1

0.333... =! 1/3

Its only a base10 approximation that is out by the same distance that 0.999... is away from 1

0.999... does not equal 1

That is an approximation moffered to high school students to keep things simple

>you are actually getting a number that is just smaller than 1 by an infinite amount
If that were true, you're assuming what you're setting out to prove.

>⅓ = 0.333...

You failed at the first line

>1/3 + 1/3 + 1/3 = 2.9999999999/3
.3333333333 ≠ ⅓
It is the closest decimals can get, but not exact

...

Wrong.

Simple. Try to think a number between 0.999... and 1.

You can't.
So 9.999... = 1

.3333333 is the best base 10 decimals can do, if you dont like it dont convert to it

This guy gets it

Simple. Try to think of a whole number between three and four.

You can't.
So 3 = 4

>inb4 (a/b)^∞ for a

there is nothing to discuss

number =/= whole number

Your post is invalid.

I can answer this precisely and accurately with one line. Question is if you are willing to accept the answer?

How about this other one I found:

1/3 = 0.333...
+ 2/3 = 0.666...
---------------------
3/3 = 0.999...

correct. end of discussion.

Just make x = 0.99
10x = 9.9
10x - x = 8.91
9x = 8.91
x = 0.99

1/3 does not EQUAL 0.333...

It.is a base 10 approximation

I won't accept it if it's incorrect.

It is by definition of the decimal expansion. It's just a geometric series.

Prove it.

And this is why you're not a mathematician.

so, tell me the number between 0,999... and 1

x=0.(9)
10x=9.(9)
10x-x=9.(9)-0.(9)=9
9x=9
x=1

1-(1/inf)

0,9999
Tadaaa~

no

At least one other guy with a higher education.

Tell me a number between i and e.

If you accep infinity in.mathematics, which you must... then you must also accept the reciprocal of infinity.

Which is the gap between 0.999 and 1

∞
∑ (3 / ( 10^i))
i = 1
The upper bounds of the limit, by definition, is 1/3

Thank you!

That's still 1

are you retarded?

Limits never actually reach the upper bound. You know this

1/3 =! 0.333...

>what is convergence

>what are repeating decimals

You can't just go and use the concept of infinity and be consistent its implications.

No its not. Its jnfinitely small, as infinity is.... well infinitely large.

1/inf is the precise definition of the gap between 0.999... where people claim no number can possibly exist therefore they are the same.

No its not. Its jnfinitely small, as infinity is.... well infinitely large.

You are thinking as infiinity as something that ends. but think it this way.

1 - 0.999... = 0.000...

You could "think" there is going to be a 1 at the end of the 000's but there is no end.

Nah. Infinity is just infinity. Not a real number, but required to be real by entire fields of mathematics.

Its valid.

As is its reciprocal.

Which destroys the assertion the 0.999...=1

Haha true, it is just an approximation.

how does that destroy it?

Just tell me a number between 9.999... and 1. It wouldn't be that hard if it was possible...

Again?

1-(1/inf)

Think about it for a second

The operation you are trying to express is known as undefined. You can't say it's between 0,999... and 1, nor you could say it even has a result.

Not the guy, but I can tell you in under a second that 1-(1/∞) is just another way to write 1, which definitely doesn't fit inbetween 0.999... and 1.
You're thinking of (1/∞), which is a valid but useless way to write 0.

I will come at this another way.

How many times are we expected to repeat the 9 after the decimal point?

I say: i will repeat one more time and that is your gap between 0.999... and 1.

Unless you are suggesting we repeat the 9's infinitely?

Which means the gap is the reciprocal of infinity.

Either way, it never makes it.

>How many times are we expected to repeat the 9 after the decimal point?

Are you kidding me? do you even know what do the "..." represent? OF COURSE the 9's are repeated infinitely. "The gap" just doesn't exist.

did you pass 3rd grade?

You can't accept infinity and reject convergence.
That is really all this discussion is about.

If you agknowledge infinity then you must agknowledge the reciprocal of inifity which is BY DEFINITION, the gap.

1-(1/inf)

Stop rubbing it in Dave!!! You fucking dick!

stop with that 1-(1/inf) bullshit. 1-(1/inf) is an undefined operation. Can be considered as 1, but it's still undefined.

So is assuming that we can stack an infinite amount of 9s after a decimal

>So is assuming that we can stack an infinite amount of 9s after a decimal

I don't even...

Yeah, it kinda is

uh, give me your lunch money? something like that?

1/3 = .33333333333...
.3333333... * 3 = .99999999999...
3/3 = 1
.99999999999999... = 1

>i dont even have an argument

I don't understand how this is even a legit question and why people think 0.9999...=1
They are very close but 1-0.999999....=/=0 so they are not equal.

1of the cups will have slightly more than the other 2 cups to make up the missing fraction of a ml

If you write it in caps, please provide citation. I mean, you claimed it is useful in "entire fields of mathematics", surely it has been used somewhere.

1-0.999... = 0.000...

Please, it's not that hard people... think of a number between 0.999... and 1, and the whole discussion is over.

You don't understand the concept of infinity.

0.9999.... With infinite number of 9 IS equal to 1, real equality.

It just that people can't understand mathematical infinity

Every time someone writes 0.999... they are assuming an infinite number of 9s.

>use:confirmed

You, idiot, are a sir.

it's not "assuming". "..." is the literal expression of repeating decimals.

You say that 1/inf is undefined yet seem fine with an infinite number of 9s

>logical dissonance

#no

Seriously. Are you fucking retarded?

So it assumes that infinity is a real?

Ie, the number of 9s is actually infinity?

Then what if the reciprocal?

1/3 ~= 0.3333333333... but ≠ 0.3333333333...
One third cannot be expressed in Base 10. Doesn't matter if there are an infinite amount of 3's behind that decimal point, it will never be one third. Infinite 9's will still end up being 0.999... not 1. 0.999... can be ROUNDED to 1, but it is not 1. You fucking clowns.

yup, you're retarded, please leave this thread

No

Lack of argument followed by ad hominem noted