[split] 0.999... equals 1

[Tiberius]

You still don't get it. You are using the value 0.999.

This isn't the value I am using. I am using 0.999... which has an infinite number of 9's on the end. It is 0.999999999999999999999999999999999999999999999999999999... (forever and ever and ever).

It equals 1!!!

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Splitting this thread up...

[leo-rcc]

No, it is 9X, 10X-1X. If you are going to multiply infinite numbers then the outcome is infinite as well. Subtraction of an infinite value will give you another infinite value.

[Violet]

It does not equal one... one will always be greater than recurring .999999.

To get one from recurring .999, you are rounding.

[Retorth]

This is quite an informative site regarding 0.99999999999 (infinite) = 1 :

http://www.faqs.org/faqs/sci-math-faq/sp.../0.999eq1/

Credit to Adrian for introducing it.

[Violet]

Not at all... 1/9 is .111, if you multiply 1/9 by 9 you fill out the fraction (one).

1/2? .5, multiply by two? 1. Therefore .5 = one?

[Retorth]

I think what Adrian is trying to say is that "0.999999(infinite) = 1" will make sense only if you do not limit the "9"'s. It's 0.99999(infinite) and not 0.99999 or 0.9999999999999 because these numbers definitely do not equal 1. As long as you limit the "9" it will never equal 1 but if its an infinite 9 then that equation pans out.

[Violet]

That's just the thing... you will never reach one with recurring nines... you will always be less than one, no matter by how little.

His equation is no more logical than any number = 1.

[Retorth]

E.g

if X = 0.99

10X = 9.9

10X - X = 9.9 - 0.99
= 8.91

It just won't work.


But if you use unlimited 9's...as Adrian showed:

We set x to 0.999... (reoccuring). 10x is therefore 9.999... (simple multiplication).

To get 9x, we need to subtract x from 10x (10x - x), which is the same as doing the calculation 9.999... - 0.999...

So 9x = 9

So x = 1.

Well, perhaps its one of those debatable things...I've only just learnt of it today so I really can't say much of it yet lol But I do find it very interesting!

[Violet]

1/9 is repeating .1111111s. Multiply that decimal by 9, and you get .99999 repeating. Multiply the fraction of 1/9 by 9, and you get one. What is your point?

.999999 repeating x10 becomes 9.99999 repeating. .9999999 repeating x9 is 8.9999999 repeating-ending with 1. Just because you can make an equation that makes a number equal to one at some point, does not automatically make that number equal to one. You can see this with 1/__ fractions: you can make them equal to 1 if you multiply by a certain number... but the number itself is not equal to one.

Watch, 1/9 x10 -1/9 is also equal to one. This is set up no differently for the same answer with a different number. You can make this same equation with any number. Watch, .5 x3 -5 is also equal to one... I take it .5 is also equal to one then?

[Retorth]

As I said, I only just learnt about this so I will gladly stand corrected. I just find it an interesting concept. I am not trying to debate it with you.