It’s still not “infinity”, whatever that is.
So you say it’s not “infinity”. What is it?
It never ends and it can never be completely written out.
A real number, unlike ∞.
No real number has a finite decimal representation. As a matter of convenience, we usually write .5000… as .5, but that doesn’t mean that those trailing zeros aren’t there.
Ah, you mean it’s an irrational number. Yes, they never terminate and never repeat, and cannot be expressed as p/q. It is not an infinite number, but that’s ok.
What you pasted in above was not a number, however–it’s an approximation of a number.
e, pi, root2, root3 are all irrational numbers. When decimalized, they do not terminate–they extend for an infinite number of decimal places. Decimalized, however, they are only approximations, and cannot really be manipulated unless they are rounded to a finite number of decimal places.
Therefore we can say that
2.71828 - 2.71828 = 0
without problems–an approximation of e minus itself. We can also say that
e - e = 0
without problems. However, when we say that
2.71828… - 2.71828… = 0
we recognize that the terms are not themselves numbers, but an approximate symbolic representation of the number e.
And hey, if you really want to see blown minds, check out the application of the Euler identity in which x=π:
e[sup]iπ[/sup] + 1 = 0
Put that in your pipe and smoke it.
I think we’ve established that our friend understands neither infinity or what a variable is. Kozmik, my advice to you is to get either a good math book or a very patient math tutor.
Andros, you got it! 
Well, yippy skippy for me, I guess.
If you had simply wanted to lay out some of the most basic ideas in mathematics, as I did, you could have done so at any time.
What’s the debate again? I still have no idea what it was you wanted to discuss in the first place.
New topic for debate:
Resolved: Have you ever looked at your hands, man? I mean really looked at them? Whoa.
*e * - e = 0
You know that; I know that.
But just to make sure 
we have our super computer solve e - e
The super computer must complete two calculations; first, the super computer must find out the exact value of e and then, the supercomputer must subtract the exact value of e from the exact value of e.
KNOWLEDGE: e - e = 0
PROOF: when the supercomputer completes those two calculations
Since the supercomputer can never complete those two calculations, we have knowledge without proof.
No - if you find anyone, programmer or not, who attempts to compute the exact value of an irrational number (and Euler proved e irrational) you fire them. Or worse.
BTW, are you scared to respond to me?
Nope. We don’t need a supercomputer to “prove” anything.
I can prove that the square root of five is an irrational number. Similarly, I can prove that the square root of two is irrational as well. In neither case do I need to calculate an infinite number of digits.
Without a computer I can prove that e - e = 0:
Additive inverses always exist for real numbers (proof available upon request)
*The additive inverse of a real number n equals (-1)*n
e is a real number
Therefore, the additive inverse of e is (-1)*e or -e
QED
I guess I’m still missing your point. This is all really basic algebra. I promise, no computers are needed to “prove” these things.
Would you like the proof that e[sup]iπ[/sup] + 1 = 0? No computer can ever demonstrate that either, but it’s a fact.
It doesn’t matter what the value of e is: e - e = 0 follows from the axiom of identity.
Bull.
As has been pointed out to you several times already, statements like “x-x=0 for all real numbers x” can be proven from the axioms of mathematics. It seems your claim is that “e-e=0” can’t be demonstrated. But of course it can. The demonstration just isn’t as simple as moving pebbles around on a counting board. Instead the demonstration consists of laying out the axioms of mathematics and the rules of logical deduction, and then showing step-by-step how “x-x=0 for all x” follows from those axioms and rules. It’s as much a demonstration of fact as taking three pebbles away from three pebbles to leave no pebbles. The only difference is that you have the option to personally reject the axioms or rules of deduction if you wish (good luck with that).
No computer ever can prove these things, even in theory. All computers have finite precision, though it can be very large if you try hard enough. Thus, no computer can even represent 1/3 with perfect accuracy. There are methods, like interval arithmetic, to understand this loss of precision, but you can never prevent it. So are friend Kozmik appears to be as ignorant about computers as he is about algebra.
This lack of precision can have big consequences. When I was in grad school there were a few students working on interval arithmetic. They had a grant from the Army Corps of Engineers to evaluate the precision of their computations about how much dirt to move around the Mississippi to keep things from flooding. The analysis showed that they were off by millions of tons - that the number they came up with was practically random. This was almost 30 years ago, and had no part in the recent unpleasantness.
Don’t look upthread. You’ll get an ulcer. 
Thanks for the heads up!
…and the definition of =, and the definition of -, and the definition of 0…
Actually, I think that is in fact Kozmik’s point (such as it is). Namely: no, computers don’t have infinite precision and therefore cannot demonstrate that e-e=0 just by subtracting one from the other. Which by itself is correct. However, Kozmik seems to be leaping from there to the idea that e-e=0 can not be proved or demonstrated by any means, which is preposterous.
I didn’t get the impression that he understood about precision, only about that any representation of e as a number does not terninate. I think he’s talking about the computation, not the representation.
Actually, since e is (1 + 1/n)**n as n goes to infinity, you could probably prove e - e = 0 by induction on this, but that boils down to something just as trivial as what we’re talking about.