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Pretty much. It depends how many significant figures the number has. If its 0.9 recurring, then for the sake of simplistic calculation it is rounded to one, unless accuracy is a necessity.

If accuracy isn't a necessity it wouldn't be quantified as 0.9repeating.

Numbers can be written in different ways and still mean the same value.

If 1/9 is 0.111 repeating, 2/9 is 0.222 repeating and so on, then 9/9 is 0.999 repeating.

9/9 can be simplified to 1.

Another way to look at it is if you were to subtract 0.999 repeating from 1, you would get zero. If there is no number between two real numbers, then it must follow that they are same number.

this is the day you learned numbers aren't real

Wrong.

1/9 = 1.111...
9 * 1/9 = 9/9 = 1 = 9.999...

They are mathematically equivalent. They are the same number.

True.

1/9 = 0.111... * my bad

1.0000 looks a lot different from 0.9999. even when i blur my eyes they don't look the same.

They are the same, though. 0.999 repeating is exactly 1. Just because 100 doesn't look like 4, it is in binary-decimal.

Pretty much. One of the limitations of a base 10 number system is that it sucks at dealing with the number 3.

0.999... is the same as writing something as 3/3 or 9/9 or 999/999.

People think that because they look different, they can't mean the same thing. We do it with language all the time:

1 = I = One = Uno = Ichi = 9/9 = 0.999...

This is like saying sky blue is close enough to navy blue, and so they're both just 'blue'
For some purposes, yes, it's close enough. But they are unique values and this means you can't munge them except in specific contexts.

0.9 repeating is exactly, precisely equal to 1. They are exactly, precisely the same number. This can be unintuitive, but stems from the definition of real numbers. Two real numbers are different numbers if they have an infinitely many of numbers between them. These two numbers don't, so they are the same number.

Also:
0.9...=0.9... |×10
10×0.9...=9.9...|-0.9...
9×0.9...=9|÷9
0.9...=1

ALSO we can define 0.9... as the sum of the infinite geometric series where the n:th member of the series is defined as 0.9×(1/10)^(n-1). The sum of infinite geometric series is exactly known (when they converge), and for this series (that is 0.9...) it is precisely 1.

0.9... is not "for all intents and purposes" equal to 1. It is EXACTLY equal to 1.

0.999... =/= 1
but
0.999... ~ 1

You can also write the number 1 as an infinite series, like 1/2 + 1/4 + 1/8 + 1/16 + ... = 1

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>1/9 = ~ 0.111...
it just depends how close you really want to get

is like how you put 0 after 1 to make 9 10

ALSO also: there's a whole Wikipedia article on this shit en.m.wikipedia.org/wiki/0.999...

ALSO ALSO: the intuitive confusion around the subject comes from the inability to cope with infinity and the unwillingness to accept that there can be many was to represent the same number. Just like I can write 2×4=8 where 2×4 is exactly the same thing as 8, I can write 0.9...=1 it's just two different was of writing the same number. If there's nothing between the two numbers (and there isn't, a number like 0.0...1 doesn't exist because that's not how infinity or infinitesimals work), they have to be the same number.

The real number line is infinitely dense, so all different points on it are separated by infinitely many points. 0.9... and 1 don't have infinitely many numbers between them, so they have no numbers between them.

0.9999...≠1 implies

0.9999...>x

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

There's mathematical proofs showing that 0.999... = 1

probably because numbers represent language

oh no, /sci/ is leaking into other boards... I guess that can only be an improvement though
also, to quote an user on /sci/:

>Here is my favorite proof: Suppose x = 0.999... If you divide by 10, the digits should move over 1 place

>x/10 = 0.0999...

>Now add 0.9

>x/10 + 0.9 = 0.999... = x

>Now it is as simple as solving the equation
>x/10 + 0.9 = x, for which x = 1.

SAVEANONHEROES

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Same with 3/3

muh dick nigga. Now give me yo btich

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Was Mathematics "discovered" or "invented"?

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>You can also write the number 1 as an infinite series
.999... is an infinite series.
9/10 + 9/100 + 9/1000 + 9/10000 + ...

Nope. There will always be something missing.

see

1 =/= 9.9999999
1 is equivalent to 0.999999999999999999999...

see

What's missing?

0.00000000000000000000000..........the eventual 1

>x/10 + 0.9 = x
What .000...1?

Wouldn't you like to know?

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yes also jesus's name is on 4 of the 9 numbers we use