0.(9) and 1

It is not truly accurate but all maths beyond arithmetic is glorified super accurate approximation so deal with it, faggot.

You behave like an animal.

For stating facts? Everyone knows that 0.999... has a 1/inf difference with 1. For what purpose would you ever require infinite precision? 10^-50 (insert any size unit really) is way smaller than any stupid fucking particle that the cern fags will ever find.

I see no point in talking to a person who does not understand that infinity is unattainable.

Sorry, but you are inadequate.

And we can not put there "=", because they will never be equal.

If we dig through Hyperreals, 1 is never equal to 0.9 or vice versa

I agree with that. By foregoing infinite autismal precision, 0.999... is equal to 1.
It isn't equal to 1 but for all practical and imaginable purposes it is.

In big boy math, what you call -> is literally just =

Wrong, it's exactly equal to 1
[math]0.\bar{9} = \lim_{n\to\infty} \sum_{i=1}^{n} \frac{9}{10^i} = 1[/math]

brainlet

The whole 0.9... != 1 meme is getting kinda stale.

brainlet

Do you know how repeating decimals are defined?

>using brainlet friendly axioms
brainlets

Express 1/3 as a repeating demical

I would if I could, bitch.

9/10 + 9/100 + 9/1000 + 9/10000...:
9/10 + 9/100 = 99/100
+ 9/1000 = 999/1000
+ 9/10000 = 9999/10000
...

( x - 1 ) / x
When will (x-1)/x = 1?
Never.

(x-1)/x = 1
x-1 = x
x-x =1
0 = 1
Absurd.

x / (x-1) = 1
x = x-1
x-x=1
0=1

ITT: People who never took Calculus.

You forgot the part where you take the limit

t. doesn't understand that calculus is about (very accurate) approximations

Seems like you failed calculus

"Approximately equal" is not "equal".

Where?

seems like you haven't finished your khan academy course yet, brainlet.

>He doesn't understand that Calculus is about infinitely accurate approximations (you literally take limits with regards to infinity all the time). Furthermore the limit function is by definition a supertask.

9/10 + 9/100 + 9/1000 + ... will never equal 1, but 0.(9) means the limit of that sum

>repeating what I previously wrote but substituted with big words seen in his text book

oooga booga me smart

en.wikipedia.org/wiki/Repeating_decimal

>Every rational number is either a terminating or repeating decimal

no
0.(9) = 0.9999... = 9/10 + 9/100 + 9/1000 + 9/10000...

And the limit is 1 (unattainable limit).

How do you write PI in decimal form, user?

...

>wikipedia says arbitrary rounding is the way to go
oooga booga
How many decimals would you like?

It's not rounded

round 0.9
1
round 0.99
1
round 0.999
1
...
but somehow 0.999... -> 1 does not constitute rounding? :thinking:

This is groundbreaking work. You're right, there is absolutely no mistake in any of this. Have you considered publishing this? Either formalize this yourself and submit it to someone like the American Mathematical Society or contact a professor and ask if this could be your PhD thesis.

What is 1 - 0.(9)?
Does 0.(0)1 = 0.(0)2?
Does 1/(0.(0)1) = 1/(0.(0)2)?

Could you latex that please?
My point is still that .999... is approximately equal to 1 and your wikipedia links and high school math text book exerts won't change that.

I'll tell you a little secret.

Idiots think that 0.(9) = 1.
And smart people think that 0.(9) ≠ 1.

I noticed this a long time ago.
And I'm saying this absolutely seriously.

[math]1-0.\bar9\\[/math]

It's funny.
If they do not understand this themselves, then I do not want to communicate with them.

Do you just not know how to take the limits at infinity? What is "unattainable limit"?

that does not equal 0. it equals a hypermeme that can't be expressed.

Infinity has no limits.

"unattainable limit" - is the classical limit, just read the definition of the limit.

>He thinks infinitely accurate and very accurate are practically the same term

The logical rigor of an engineer, ladies and gentlemen

Are you saying it equals a hyperreal number? What is a hypermeme?

infinity is not a real thing, therefore infinite accuracy doesn't exist. When the infinity illusion fades for you (if it does), you'll realize how much of a brainlet you are.

Is 0.(9) a real number?

Yes
1 - 0.999... = .000...1
which is an impossible number that can not be expressed properly, ie hypermeme territory.

>infinity is not a real thing
>I have defined all concepts of reality to be finite with my mortal mind

ho-ly shit

Look everybody, he's worse than an engineer

That means, according to you, 0.(9) is also not a real number. So what type of number is 0.(9)?

I am guessing 0.(9) is 0.999...
It is an integer (1) subtracted by a hypermeme.
whatever brainlet

>It is an integer (1) subtracted by a hypermeme
Which is what type of number?

undefined, which is why assumptions about rounding up to 1 is not correct (but for all real purposes is)

Then how do you define repeating decimals if you don't accept the current definition of repeating decimals?

an infite series never ends. 0.999... does never end. Therefore it never becomes 1.
To make 0.999... equal to 1 you must add a hypermeme number equal to 0.000...1
which does not exist. Theorycrafting about impossible series and their relationship to the real world is a waste of time, which is why brainlet math nerds invent axioms that allow operations on infinite series, to be able to get a result with near infinite precision.
It is not correct to say that 0.999... equals 1 but it works out in the end because there is a limit of how much precision is really necessary.

...

The notation in the op is such fucking garbage I want to blow my brains out

>infinity has a time factor, it's like a steamboat willie cartoon, whistling as it goes

kill yourself

You are retarded and don't know what a limit is. The reason we can't say an infinite sum is equal to anything is because we cannot perform infinitely many operations HOWEVER this is where we can use limits. Limit shows you a bound which your increasing sum/function/whatever cannot increase past. So the limit of 1/2 + 1/4 + ... is 1. When we say sum from 1 to inf of whatever we mean taking the limit of the partial sum 'function'. When people say 0.999... they usually mean the NUMBER they got when they took the limit of 1/2 + 1/4 + ... Keyword here is that they're talking about a number. What you are talking about is a sum which converges to that number and then you claim that 1 converges to itself genius.

9/10 + 9/100 + 9/1000 ... = sum from n=1 to inf of 9/10^n = limit m->inf of 10^-m (10^m - 1) = 0.999...

0.999... is a NUMBER, A BOUND, NOT A PRODUCT.

0.999... = x
9.999... = 10x
9 = 9x
x = 1

0.999 (NUMBER) is the same as 1 (NUMBER).

No, you are just as retarded as them.

A real number is an equivalence class from the set of equivalence classes of Cauchy series of rational numbers.
By that definition it instantly follows that 0.999...=1, since being in the same equivalence class is the definition of equality.

>The reason we can't say an infinite sum is equal to anything
Wrong, we can.

>0.999... is a NUMBER, A BOUND, NOT A PRODUCT.
It is an equivalence class of series.

>When people say 0.999... they usually mean the NUMBER they got when they took the limit of 1/2 + 1/4 + ... Keyword here is that they're talking about a number. What you are talking about is a sum which converges to that number and then you claim that 1 converges to itself genius.
The number or the set of equivalence classes are the same, by definition.

>an infite series never ends. 0.999... does never end. Therefore it never becomes 1.
False by definition.

>if 2 real numbers only differ by an infinitesimal they are the same number

>0.999... can be expressed by a limit of the series 9/10 + 9/100 + ....

>1 - 9/10 - 9/100 - 9/1000... -> 0 to they are the same number

thanks genius

and no we cant say infinite sum is equal to anything

brainlets

>>if 2 real numbers only differ by an infinitesimal they are the same number
"infinitesimal" is not part of standard mathematics.

>1 - 9/10 - 9/100 - 9/1000... -> 0 to they are the same number
Yes, by definition.

>and no we cant say infinite sum is equal to anything
By definition it is.

I actually know what a real number is, unlike anyone else in this thread.

mathlet

0.999... = y
9.999... = 10y --- error.

10 - a number
infinity - not a number
infinity = green color (just an example)

10 x infinity = 10 x green color ≠ green color
We can not multiply them.

0.999... - an "infinite number".
An "infinite number" is not a number.
An "infinite number" is a red color.

0.(9) = y
10y = 10 x red color ≠ 9.(9)
We can not multiply them.

>9.999... = 10y --- error.
Wrong by definition.
You are working outside of standard mathematics, nothing you say has any relation to anything else in mathematics.

Their "proofs" are stupid, as they are inherently self referential, 0.99...=1 is true, simply by definition.

There is no infinity going on here. Limits are not infinity. Learn what they are.

please show me some quote or source or anything which clearly says that we can sum an infinite amount of things

>please show me some quote or source or anything which clearly says that we can sum an infinite amount of things
What do you mean by "can".
It is defined that way.

As for its occurrence in standard mathematics:
en.wikipedia.org/wiki/Series_(mathematics)

>9.999... = 10y --- error.

What is 9.999.../10 ?
Is it 1 ?

One idiot has long invented a stupid theory, and other idiots still believe in it.

>One idiot has long invented a stupid theory, and other idiots still believe in it.
That is a disagreement mathematicians had for a long time.

If you want to be an ultrafinitist go ahead, nobody is stopping you, but for the love of god never try to explain real numbers again.

red/10 < 1 or > 1?

I see the misunderstanding now. Basically we're taught that we can sum series without actually summing them (without performing the operation) by taking the limit and assigning its value. Same thing with calculus and dividing by 0 problem. We can see what the result is without performing the operation. It's just a choice of words I guess.

If you want to invent your own finitist theory then go for it but in such theory all real numbers except the rationals would not exist.

oh well, you tried

...

Yes and you making up your own new model doesn't change the existing one.

I know.

We can not reach infinity in reality. I'm trying to create a model that describes the reality without the old errors.

Do you still not idolize me? :(

I can not use the name "real numbers".

And I will not use the name "super real number" because it's schizophrenia.

Then I will use the name "D-numbers".
The numbers of Dubovitsky (my last name).

Nobody is against?

x = 1 - 0.(9)

what is the value of x?

1 / x = infinity

therefore x = 0, so 1 = 0.(9)

You can respond to people by clicking on their name.

>We can not reach infinity in reality. I'm trying to create a model that describes the reality without the old errors.
Okay, whatever floats your boat.
This is a philosophical position.

Of course not.
You have done nothing.

>I can not use the name "real numbers".
Nobody cares about your crackpot theories.

>Nobody is against?
Delete your thread.

Holy shit, you are retarded.
Please learn a bit of math before responding.
You are nearly as dumb as OP.

Do you guys never get tired?

haters and sociopaths :)

I have already proved that they are not equal. Therefore, there is no point in continuing to argue.

>I have already proved
No, you redefined terms.

>there is no point in continuing to argue.
There never was in the first place.
You said nothing of worth and made no argument.

This, op just didn't know what repeating decimals represented

Also, it's "have proven", non-English friend

I assume all these threads are bait but kill yourself anyway.

and other

just read:

Have you finished high school?
lim x->inf (x-1)/x = 1 you faggot