actually, its not 1. its almost 1, but not quite. if it were 1, it would just be 1.
1 = 1. .9999999999… = .9999999999…
100 x 1 = 100
100 x .999999… = 99.99999999…
plug it into a calculator.
How can it be “almost” 1? Since 0.999… repeats forever, there’s technically no number (regardless of how small) that seperates it from 1. Since there’s no difference then between 0.999… and 1, they’re the same number. Again, it just comes down to decimal math not being able to properly handle infinite values. It’s a head-scratcher, but the official conclusion is that 0.999… = 1.
Not by my calculations. 1.0 - 0.333… = 0.666… (repeating forever), which is exactly 2/3.
1 is not 0.9999…
just like 1/3 is not 0.3333…
the reason is 1 can never be divided into 3 exact parts but 1/3 still exists because you can get numbers very close to it such as 0.3333333333333
it all depends on how close you need to get to 1/3
calculus can’t handle infinite because infinite is undefined which is why i think its wrong saying 0.3333… * 3 = 0.9999… = 1
First lesson in calculus: Forget about the calculator. Calcs are for numerical calculations. There are two ways to understand why 0.999… = 1.
Atheist explained the simplest way: accept that 0.999… stands for 3 * 0.333… = 3 * 1/3 = 1. The second way requires that you learn about limits and the definition of a limit of a function. Most people find it boring and difficult, especially the definition. Now 0.999… means the limit of 1 - 1/10^x when x-> infinity.
To get an idea what the limit is, study this:
1 - 1/10 = 0.9
1 - 1/100 = 0.99
1 - 1/1000 = 0.999
The larger the number is the closer to 1 you get. But you will never get to 1 or past it, just infinitly close. We conclude that 1 is the limit of 1 - 1/10^x when x → infinity.
but ~ is undefined
its like
1/3 = 0.33333~
~ = what ever number of 3’s it takes untill the number is equal
no matter how many 3’s you put you will never get an exact 1/3 because 1 can never be divided into 3 exact parts, that can be proven via geometry.
the more 3’s you put in 0.3 the closer you get to 1/3 but it will never be exactly it, its accurate to say
1/3 ~ 0.3 (here ~ means proximity not infinity)
Because even 0.34 is bigger than 0.3333333333…
math sucks. and you’re all wrong. like i said. if it was 1, it would be 1, and not .999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999…
Now that just hurts. Some of us may enjoy calculus. (not me but it brought up my gpa 
)
On a sidenote, how many of you have taken a calculus class, how many, and what was the highest one you took?
I just finished multi-variable calculus, it was my third calculus class.
Trying to make the anti-math forum members feel inferior, hunh? 
Just joking, of course.
*Okay, back to the question (for those who can actually answer it).
No just curious seeing as calculus seems to come up alot in this topic. And anyway I don’t like it anyway, I’m forced to take it in engineering, hell by the time I get my degree I’ll have a total of 5 calculus classes done.
Goes off to play with a calculator
the thing is that lot of people say 0.99999~ =1 because there are no numbers in between them
what i say is that ~ is undefined, by the definition used here ~ = the number of 9’s it takes until 0.99~ = 1
which is wrong because no matter how many 9’s you put it will never be 1 therefor ~ is a non existing number
it seems strange to me that in America there are lessons on just calculus. We have… well… maths. At the A-level level I do Pure Maths and Stats. I’ve just now been lurning about “curves defined implicitly”
eg y^2 + 2x = 4
–> 2y dy/dx + 2 = 0
dy/dx = - 2 / 2y = -1/y
(but more complicated, heh)
Me too, and several other math classes. Math is only fun (if ever) once you’ve already learned it.
I just have to answer this. So I’ll make this my last post.
0.99999999999999999999999999999… does not equal 1.
Here’s why:
1/3 (1 dived by 3) = 0.33333333333333333333333333333333
2/3 (2 dived by 3) = 0.66666666666666666666666666666667
3/3 (3 dived by 3) = 1.00000000000000000000000000000000
It is because 2/3 is not 0.666 recurring forever that 3/3 is allowed to be 1.
the problem with that number is 1/3.
this makes three equally large parts, but the problem is that it is impossible to calculate this number, as the standard form of dividing numbers will have one left over, no matter what. therefore you get:
0,33333333333333333
0,33333333333333333
0,33333333333333333
these three parts are the components of 1, but there is a residing piece left, that will not fit in without making one of the parts larger than the other two. that is why people say that 0,9999999999999… equals 1. this is fundameltally wrong, because the residing piece is not factored in. the number x,9999999999999999999… , where x is any number equal to or greater than one, and … is a symbol of infinity, will not be equal to anywhing else than what is written. the reason people dissagree is because there is no way to write the answer to 1/3 correctly. the number we write is the closest answer we can find, but it is still wrong. if you should just write the number 0,99999999999… without it being the answer to 1/3, then you would have to assume that the number is correct, and that makes it impossible to say that it is equal to 1, as that would mean increasing it’s value.
simply put, it isn’t the number that is wrong, it’s the method of finding it.
No it’s not. You’ve just rounded that number, which is incorrect.
2/3 is 0.666…
The key here is to remember that the 6’s are repeating FOREVER. It’s a hard concept to grasp, but “forever” means it does not end. Conventional math falls in a heap when you introduce things like “infinity” (a concept that doesn’t exist in RL), which is where you get discrepancies like 0.999… equaling 1.
It’s not a matter of opinion - this is an OFFICIAL mathematical fact, and the people who eventually worked it out are a LOT more equipped to do so than we are.
i never thought that this topic would still be around!
I actually do play with mine. its a ti-83+ graphing calculator. I play games(such as pacman, galaga spoof Phoenix, dance dance revolution), write programs, and draw on it as well as do math and stuff.
Solve this:
1 divided by 3
Use long division.
1/3 and .33333… are equal.
You may just disagree with the representation.
That’s another story.
And let’s not be too critical.
Anyway, math is practically hypothetical.
Would you like to talk about numbers that don’t exist?
How about 4D shapes?
Yeah, craziness.
And let’s not even mention physics…
Damn me!
Well spotted Athiest, never turst your computer or calculator.
Look at it this way. 1 dived by 3 is 0.333 recurring. So 3 lots of 0.33 recurring is not 0.9999. Therefore 0.99999 recurring is not 1.
As nitent said, 0.999 recurring is 0.999 forever, and is not 1.
It is an inibility for the 10 base system to express a value, and instead expresses an infinate value.
Asuming that a decimal point after another decimal point was base 2. You could express numbers inbetween each other like this.
0.33333333.1
0.66666666.1
0.99999999.01
Convert it into standard 10 base = 1
Technodreamer: It depends on how you define the … or the ~. If you define it as just recurring for n number of digits, you are right. No matter how many digits you won’t reach 1.
But if you define the “…” as the limit when the number of digits goes towards infinity, 0.999… equals 1. “Limit” is another definition in calculus, one that is set in stone since many decades. Good luck challenging that.
What I heard is that limits were defined after most of calculus was done. Before that they just spoke of “infinitly big” or “infinitly small” stuff. But limits now provide the foundation for the rest of everything. If you don’t like the idea you’ll have to provide another foundation for calculus! Again good luck, and have fun. 