Especially for large values of .99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999. 
Lucwarm (and others),
You cannot use ‘normal’ notation to deal with infinite series. Infinity - 1 is infinity. Infinity divided by 2 is infinity. You must be very careful dealing with infinities because you get very counter-intuitive results.
For example, you can get a container of infinite length that has a surface area of 2 square feet. Another is irrational numbers vs. rational numbers. Between every two irrational numbers there is a rational number and between every two rational numbers there is an irrational number. However, for every rational number there is an infinite amount of irrationals that can be mapped to it. This means there is more than one infinity, different ‘levels’ so to speak. Another weird result is that subsets of infinites can be the same ‘size’. For example, consider the infinite series 1,2,3,4,5,… and 2,4,6,8,… Now 1 maps to two and 2 maps to four etc…they are the same ‘size’ in that they map 1-1 with each other!
Do not try to use common sense as it can lead you to trouble, infinities must be explored mathematically with great caution.
Another part of the argument between people here is some people ‘complete’ an infinite operation, like 9/10+9/100+9/1000… to be 1 while others will not complete an infinite operation. This is why some people will say it will never equal one but will get very close. These people are not ‘completing’ the infinite number of steps and this is not a dumb argument. Could you or any machine complete an infinite sum??
However, completing the operation invokes calculus and calculus has been shown to be very useful over the years 
Blink
oops, volume of 2 cubic feet, not area. I can’t remember the specifics anyway I just remember being fascinated when I saw it.
How so? How can infiniti * X * Y not equal infiniti? Unless you’re using negative exponential values for X or Y (which would be one strange looking countertop)…
I don’t see how you go from an infinite number to a real one… . . . . . . .
wow, what a concept 0.9rep factorial is equal to 1…
True in terms of basic (non-transinfite) mathematics…
But say, surreally, is this true? Hmmm…
I’ve been to some of Conway’s lectures. Aside from being rather eccentric, he is also highly entertaining.
[aside]
Are you maybe thinking of Gabriel’s horn, the figure you get by rotating f(x) = 1/x, x>=1 about the axis? It has a surface area that diverges logarithmically and a volume of Pi.
[/aside]
Well isn’t there the concept of an infinitesimal which is infinitely small number? I suppose it could be thought of as 1/infinity. So how about infinity * infinitesimal * 2?
No, but we don’t know the exact answer!
I was hoping nobody would get this far 
One of the current problems with surreals is integration. People have come up with excellent (and consistent) ways to extend exponentiation, square roots, logarithms &c. to surreal numbers. But integrals don’t work quite so well. Every time someone proposes something, it’s either internally inconsistent, or it gives the “wrong answer”, i.e., there’s some integral which gives a different answer under surreal integration and your usual Lebesgue-Riemann-Stieltjes-whoever integration. (This is why physicists don’t use surreals yet. Once there’s a consistent surreal integration method, they’ll be jumping all over them; you heard it here first.)
And the Gamma function (the extension of factorials to the reals) is defined as an integral. So defining (1 - 1/omega)! is non-trivial.
There is a second approach; Find the Taylor expansion of the Gamma function about x=2 and use it to calculate Gamma(2 - 1/omega). This requires knowing all the derivatives of Gamma at x = 2. I don’t know if we know this. (The first derivative is 1 - gamma, or about 0.428.) So a good first approximation to (1 - 1/omega)! is 1 - (1 - gamma)/omega.
Mathematicians cheat. If they didn’t they’d all be standing on street corners unwashed, unshaven, and mumbling to themselves. Begging for change.
Give them a problem they can’t solve and they say something like “There ain’t no problem, .99999… = 1”. And then they prove it.
My friend the math junkie told me that there is no infinity, but we need it to try to understand other things.
Surreal indeed.
The difference between .99999… and 1 is as infinite as the 9’s.
However, you’ve ignored the gauntlet already thrown down by more than one person, namely: If 0.999(rep) does not equal 1.0, then there must be numbers between them. So, if you maintain that 0.999(rep) does not equal 1.0, name a number between the two.
It’s obvious that there are two sides to this argument:
**Mathematical, adhering to the Laws of Proofs, and
The Definative, adhering to the Rules of Meaning.**
Infinity: continuing forever without end.
MATHEMATIC PERSPECTIVE:
If .999999… is guaranteed to never end, it will always equal 1.
DEFINATIVE PERSPECTIVE:
If .999999… is guaranteed to never end, it will never equal 1.
Infinity, in all essence, is a mathematic/physical anomaly. It should be considered by all to be a postulation, due to it’s unfathomable nature.
It’s not simple to imagine the purpose of infinity, but it’s easy enough to picture an endless stream of 9’s. I am sure we would all agree that 0.99999…would never end, as it is an example of infinity.
What I would like to ask now, to the Mathematic persons here, is:
- Do you consider .999999… to be infinite?
- Do you consider 1 to be infinite?
If you answer YES for question 1 and NO for question 2, then by mathematical AND definative reasoning, you have just told yourself that they are not the same number.
Do all the Definative folks agree? (high five!)
But somebody already did.
It’s the assumed number that lies between them if you take away the assumption that they meet (become the same) in infinity. You take away the proof
Call it diff…
Peace,
mangeorge
There seems to be some confusion over infinite decimal representations here. .999… and 1 both have the same length representation in decimal. It just so happens that for 1, all of the digits are zero after a certain point. So in that sense, both are infinite.
Again, I refer to my earlier series proof. Why hasn’t anyone touched this?
Even if we assume the existence of infinitesimals, there is no number between .999… and 1, because they have already been shown to be equal.
The fact that .999… = 1 is not an assumption. It’s provable, from the axioms of arithmetic, the definition of a decimal representation, and the rules of analysis.
Because the mathematical proof is beside the point. The only way to write 1 is 1. One is a single point on the number line, and can only be represented by one. No matter how you manipulate the numbers to make it appear that 0.999… is equal to one, it cannot be. Only one can be equal to one.
But the zeroes after the 1 have no value, and the nines do.
2 - 1 = 1.
10[sup]0[/sup] = 1.
ln(exp(1)) = 1.
9/9 = 1.
The integral over the whole real line of the normal density function is equal to 1.
For x > 0, |x|/x = 1.
Now what’s the difference between these different representations and the sum from n = 1 to infinity of 9*(1/10)[sup]n[/sup]?
Yes. They have a value that sums to exactly one, just like the zeroes after the one.
Oh, well, sorry - I’ll be reading this for amusement from now on…
Sheesh, if you’d said this in your first post I wouldn’t have wasted my fucking time.