Inspired by the "0 = even" thread....9999~ = 1?

[Theeloved1]

I'll just ask the basic question before quoting stuff from other sites...

Does .9~ (repeating) = 1?

 

[mickeyfan2]

No. It would round up to 1 but could never be 1. It would always be a tiny bit below 1.

Example:
.9999999999999999999 would be off by .00000000000000000001

not much, but still not 1.

 

[Sparx]

it is not one. but it would be rounded up to one for all practicle purposes.

 

[MOMTOCUTESTDOGEVER]

Actually, a mathematical proof shows that .999 (to infinity) = 1.

Here's how:
Let's assume some variable, call it x, equals .999 (to infinity):

x = .999 (to infinity)

If you multiply both sides of the equation by 10, the equation remains balanced. The result is:

10x = 9.999 (to infinity)

Now, subtract the first equation from the second:

10x = 9.999 (to infinity)
- x = .999 (to infinity)
_____________________________
9x = 9

Solving for x, we get x = 1. Substituting this into the original equation we get 1 = .999 (to infinity.)

Or, how about this:

The fraction 1/3 = .3333 (to infinity.) The fraction 2/3 = .6666 (to infinity).

Well, 1/3 + 2/3 = .3333 (to infinity) + .6666 (to infinity), so

1 = .9999 (to infinity)

 

[Theeloved1]

Actually, a mathematical proof shows that .999 (to infinity) = 1.

Here's how:
Let's assume some variable, call it x, equals .999 (to infinity):

x = .999 (to infinity)

If you multiply both sides of the equation by 10, the equation remains balanced. The result is:

10x = 9.999 (to infinity)

Now, subtract the first equation from the second:

10x = 9.999 (to infinity)
- x = .999 (to infinity)
_____________________________
9x = 9

Solving for x, we get x = 1. Substituting this into the original equation we get 1 = .999 (to infinity.)

Or, how about this:

The fraction 1/3 = .3333 (to infinity.) The fraction 2/3 = .6666 (to infinity).

Well, 1/3 + 2/3 = .3333 (to infinity) + .6666 (to infinity), so

1 = .9999 (to infinity)

and let the debate begin...

This is like the "airplane on a conveyor belt" on another forum I frequent.

 

[Planogirl]

One problem I see with that is that multiplying x=.999 by 10 would actually be 10x=9.99 if I'm not mistaken.

Subtract x=.999 from 10x=9.99 (which I never saw in practice but still), you would get 9x=8.991 and x=.999 again.

Is my math off somewhere?

 

[damo]

One problem I see with that is that multiplying x=.999 by 10 would actually be 10x=9.99 if I'm not mistaken.

Subtract x=.999 from 10x=9.99 (which I never saw in practice but still), you would get 9x=8.991 and x=.999 again.

Is my math off somewhere?

You are missing the infinity part. When you shift the decimal point the part after the decimal remains the same. So when you subtract, the part after the decimal point disappears. ex. .99999999 (to infinity) X 10 = 9.99999999999999 (to infinity). That's the problem with working with infinite "numbers", are they really numbers and can you perform mathematical operations to them?

Although there have always been many different "proofs" that 1 = .999 (repeating), the problem is that these proofs always assume that .999 repeating to infinity is a number, where in reality it is just a concept.