0.9999... = 1

0.9999... = 1

Discuss

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wolframalpha.com/input/?i=.9 repeating = 1
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1/3 = .333
1/3 + 1/3 + 1/3 = 3/3 = 1/1
kys

it doesn't equal it exactly but for most practical applications the difference is negligible.

if its an infinite series of 9s, then thats the idea.

It doesn't though. I don't care what anyone says. Being infinitely close to something implies that it still isn't that something. Therefore .999... will never equal 1.

It's true

Anyone who says otherwise is retarded

No, u dumb fuck. It is equal exactly

Every number has two ways of writing it.
1 can be written as 1, or 0.999....
1.5 can be written as 1.4999...
Etc.

oh ok

That's the stupidest thing I've ever heard.

But it's try. If u want to, I can explain it to u

but is true

>That's the stupidest thing I've ever heard.
It is not.
For example I can write That's the stupidest thing I've ever heard or 1h4t'5 1h3 5tup1d35t 1h1ng 1'v3 3v3r h34rd.

everything can be numbered! :D:DD:

STOP BE SO UPSETTI
JUST WRITE YOUR NUMBERETTI

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

shove that info up your ass and gtfo retards

Rolling for result

The answer is 40

you dont need to explain. you need to prove.

9+1=10
0.9+0.1=1
0.99+0.01=1
0.999+0.001=1
now imagine a countable infinity of nines after the .
if it is countable, we can just add a number that has as many digits after the . as the number of elements in our countable infinity. like 0.000000.....01
add them:
you get
0.99999....9+0.00000....1=1
this means to write one as 0.999999

you need an uncountable infinte number of nines after the 0.

q.e.d.

And whats with 1.00000...1?

i study math in my 4th semester and it is true that 1=0,9999...

0,999999 is getting closer and closer to 1 with every 9 you add. but technically it cant reach 1 ever. But infinity is something different.

x=0,99999...
10x=9,99999...
10x-x=9,99999...-0,99999...
9x=9
x=1

cool so what do you think of my interpretation ?
i study not math bur other natural sciences.

Stop freaking out, infinities are crazy like that

x = 0.9
10x = 9.9
10x = 9+0.9
10x = 9+x
9x = 9
X= 1

So 0.9 = 1

the concept of limits and infinity is the key here. it seems counter intuitive because 0.9 < 1 and 0.99 < 1 and 0.999 < 1 and so on no matter how many 9s we add, so long as there is a finite number of them.

0.999... represents an infinite number of 9s

>x = 0.9
>10x = 9.9
cant multiplication

dude .... whats 10*0.9 again ?

And what's with this?

If x = 0.9 then 10x = 9

learn to multiply

11

yeah but an uncountable infinity right ? Have i shown it correctly senpai ?

i mean... there exist also countable infinities, but that wouldnt be sufficient to get 1=0.999999....

You cannot simply convert float to integer

1/9=.11111111
2/9=.22222222
:
8/9=.88888888
9/9=?

one cannot simply march into mordor. its dark.

Discuss if 1.0000...1 is 1 too.

math phd here

looks different so not the same

ur all welcome

/thread

its not,by definition. simple as that.

Only if it's rounded up..

So 0,000...1 to less is okay but 0,000...1 too much not. Why? I say 1.0000..1 is 1 too

Either you are really that dumb, in which case I will point out he is a painfully obvious troll, or you are a troll as well, in which case you can eat shit and die.

.999... (.9 repeating) is EQUAL to 1 regardless of what you asshats say.

I'm not the poster but I do know some Math.

The proof is ment for x=0.999999999...
0.9 takes lesser space than an infinite amount of nines though

this

>ends with 1
>ends
This implies a countable infinity, thus not equal to 1

This is now a cringe thread

0.99999... + 1 = 2
0.9999... + 1.0000...1 = 2

So 1.0000...1 = 1 too

Dude the proof yes. but the person i was referring to meant to "debunk" the proof.
And i said to him he cant multiply. simple as that.

I know what it was meant for.

This

the problem is that at some point it ends with a 1. if it ends, you have a different kind of infinity

First of all, it is 1.00000...0(9)
All of this is seems legit, but kinda wrong. Don't fuck with infinite numbers, its stupid.
There is 2 right ways to prove that 0.(9)=1.
First one:
What is a number 2, for example? It is a line which consistcs of two untits of length. So 3 consists 3 UL (I will call them that way cause don't know how to say eдиничный oтpeзoк in english) and so on. But there is also numbers like 2.5 . So it is 2 UL and something else that is less that UL but greater than 0. Then we divide our UL into 10 equal pieces and count, how much of them we got. Then if there is something else we will divide our UL in 100, 1000 and so on pieces.
So, what is a 1? Well, it is 1, obviously. But it is also 0 and 10*0.1.
So we got 0.something. But 10*0.1 is 9*0.1 and 0.1.
So we got 0.9 and someting and 0.1. But 0.1 is 10*0.01 and it is 9*0.01 and a 0.01.
So we got 0.99 and something. So, after an infinite numbers of steps we get that
1=0.99999999.....
Exactlu.
Second one:
picrelated. Cyммa бecкoнeчнoй yбывaющeй пocлeдoвaтeльнocти.

/thread

Look proof

Close enough that I don't give a fuck

0.999... + 1.000...1 = 2.000...1

Please write me the number that is less than 1, but is as close to one as you can get.

That would be 0.999...

However, the LIMIT process of 0.999.... = 1.

It depends upon the context of those three little dots, ya know?

In the first example, it is a completed number (like pi can be), and in the second example, it is a classic limit process like you find in Calculus I.

...

So is my proof that you need an uncountable infinity correct ?

Im still strugling here if its correct dude.

i need to know.

What is 9+1?

since when is basic math knowledge cringe worthy?
Seriously, read more or something.

0.999... = 1 regardless of context

your lack of knowledge in basic math is amazing

No.

Write me the number that is less than one, but as close to 1 as you can get.

Go.

You are just pissed because im right.

Huh?
No, it's not correct. By having ANYTHING after ... you are implying the infinite number of zeroes between the decimal place and the ending digit are a countable infinity. This means it is not the same as .999... being equal to 1

Is 1 - 0.000...1 = 1?

>"as close as you can get" on a continuous number line.
kek

Wrong because the function where x approaches 1 from the left does not include the point "1" in it's domain. nice try though. learn to limit.

And is then 1 - (Infinity) * 0.000...1 = 1?

right about what?
You didn't even make a statement that can be correct or incorrect.
You simply quoted a post out of context and frankly I don't even understand what you are implying.

I'm not mad, just disappointed the average intelligence of Sup Forums has plummeted so much over the years.

you're getting hung up on infinity my dude

Who cares there's no practical application for this because nothing is infinite in real life except OP's dick sucking capabilities

9 + 1 = 10
but that doesn't ever apply here

.999...8

Here you go.
a decimal place followed by a countable infinity of nines ending with an 8. That is the closest to 1 you can approach without equaling 1.

calculus much?

So 1 - 0...00001 = 0.999... = 1
So 0.00..1 has to be Zero because 1+0=1
So 1+0.000..1 = 1.000...1 = 1

* 1-0=1

>no practical application
sure, probably not in YOUR life. I'm assuming your day job is something humble like waste disposal or retail.

Aaah my bad. I didn't have the energy to read the entire thread from the top.
Here, have a bird for the suffering and inconvenience

i'm just asking for someone to write down the simple, easy representation of the number that is less than one, but as close to one as you can get.

Just simply write it. Do it. doooo eeeeet.

Yeah. And this ive shown to lead to a contradiction which means that you need a UNCOUNTABLE infinity, just as you said. that was my proof that you need at least an uncountable infinity.

it was this...
is it wrong ?

Flaw in the first statement.

1 - 0.000...1 does not equal 0.999...

.9 with a line over it indicating it repeats endlessly.

_
.9

Just like 1/3 = .3 (repeating endlessly)

First line of the proof is incorrect.

So what is 1 - 0.00..1 then?

If you assume infinitesimal numbers to actually exist, 0.999... does not equal 1 and neither does 0.999...8

The thing is infinitesimal numbers do not exist in modern mathematics

someone already did

see

What you're thinking of OP is ℵₒ.
(Aleph-Null)
A transfinite set of natural numbers.
It does not equal 1. Because it will never reach, 1.

0.99999/3=0.33333
1/3=0.33333
case closed

a number slightly less than 1

wolframalpha.com/input/?i=.9 repeating = 1

/THREAD

Which is what number? The number most slightly less than 1 is 0.999...

this means that 100% (3/3 or 1/1) is 0.999999...
not 1.
Idiot.

>wolframalpha.com/input/?i=.9 repeating = 1

Incorrect. Wolfram Alpha is affected by a mathematical exploit of digital computing.

It will claim 'true' to avoid deadlocking a calculation. (Because it will never matter in practicality.)

either this is a troll or you are abso-fucking-lutely retarded

Don't panic, but it's 42.

the problem is if 1 is exactly 1 then 1/3 is not exactly 0.(3).
Is that what you mean ?

no, because 0.999... = 1

they are the same number written two different ways.

you can't just use mathematical notation to mean whatever you want. you have to follow the rules of the game

0.999... does not mean some really big but ultimately countable number of 9s

This. It would infinite calculate otherwise.

0.999...8
No I disagree.
Because then I can create a smaller number
0.999...89
See how that works?

I totally accept your formalization of an infinite string and then addition to the end of that string. But here's the kicker...

Once you accept that formalization, then what directly comes into play is infinitesimals.

Between it takes an infinite amount of infinitesimals to make the smallest real number. That's their definition, right? Right.

So by your own formal argument, I can create a number between 0.999... < x < 1, showing you that 0.999... does not = 1.

0.999... < (0.999... + dx ) < 1

That's 0.999... plus an infinitesimal.

And by using the infinitesimals (which is a core concept to your limit process), that is the only way we can get to the "end" of your infinite string without the ability to add another unit to the end of it.

This is why the Fundamental Theorem of Calculus, that wonderful epsilon-delta exercise we all know and love, is all about an interval around the limit number, and not about being equal to the number itself.

>mathematical exploit of digital computing
as a programmer and security analyst, this phrase makes me cringe.

What are you even saying, nigga?
I understand your point is that it would try to avoid infinite recursion, but that isn't why it says true. It says true because it's fucking wolfram alpha and it was asked to verify a simple equation; the answer to which is universally known.

If it's breaking from a "loop" it would say false, not true... but stuff like this is a mathematical axiom and it's programmed to know the equality. It's not calculating anything when you ask if 0.(9) = 1.

yes