The infinite number of nines will still be less than one. You'll have to remove the decimal point completely to get to one. As in, a decimal point, then a billion nines is still less than one.

The number of nines is irrelevant, it'll always be less than one.

A billion nines is less thamn one. Infinite nines is equal to one.

The number of nines is irrelevant, unless it's an infinite number. Then it's one. No matter how you look at it mathematically.

1/9 = .1111...
9/9 = .9999... = 1

10x = 9.9999...
x = .9999...
9x = 9
x = 1


This seems to be what you are doing.

:lol: This may never die.

Approaching the problem for another angle.

1 - 0.9r = ?

either = 0 , or = 0.000r1 (that is, an infinite string of zeros with a one at the end. Which I know makes no sense, but this is maths so never mind)

So what does happen if you divide one by zero?

either 1 / 0 = 0
or
1 / 0 = 0.0r1

My intuition is the latter. Which makes me think that 0.0r1 is a coherent concept, and that it is the difference between 0.9r and 1.

Yes, I just divided by zero on the 29th of February, 2012. WTF am I doing? :lol:

Zero. If there are infinite zeros, there is no end for there to be a one on. Neither. Are you claiming that 0.0r1 x 0 = 1?As you seem to be aware, division by zero is not possible.

:facepalm:

Total brain fart.
I was thinking about dividing by infinity.

Ahem...

And in response to
I think this is an impossible construction.
Infinity is not a number. It is a concept defined in terms of numbers but it is not itself a number. No number is infinite.

Right. Infinity is not a number. So all examples of a billion nines, or a billion zeros followed by one, do not apply.

So if 0.0 is followed by infinite zeros, you can't put a one after it. There is no "after it". 0.0r1 = 0.0r = 0.

Therefore 1 - 0.9r = 0.0r = 0.
One divided by infinity = 0.0r = 0.

ftfy
Ok, thats all I got.

I'm not convinced by that.

We define i as the square root of minus one, despite the fact that there is no number which can be multiplied by itself to produce minus one.

I see no reason to not define "infinitesimality" as 0.0recurring01.

Mathematicians just make shit up all the time, but they call it "stipulating". Why can't I? :p

Let's do some math with 0.0r1

10 x 0.0r1 = 0.0r1

(10 x 0.0r1) - (1 x 0.0r1) = (9 x 0.0r1)
0.0r1 - 0.0r1 = ( 9 x 0.0r1)
0 = ( 9 x 0.0r1)
0/9 = 0.0r1
0 = 0.0r1

So even if we stipulated that putting a one "after" infinite zeros was syntactically meaningful, it would still equal zero.

That's why it's an imaginary number.

When you have a PhD in a field no one can understand, you can get away with a lot. Hell, they got the New Math over on us. It's all gravy from that point forward.

I'm trying to remember why this is in the Products ... thread. I'm too lazy to go back and search for the origin.

This.

cause they're timesing some numbers.

:Long hard stare:

even by my standards, that was pretty bad. :D

Maybe there should be a subforum...or even just a thread for all the mathiness that goes on around here.