Are you deliberately excluding the extended reals from consideration?
More accurately, then, no computer can manipulate .3333333… in that form, as it’s nonterminating.
It doesn’t have to, of course. That’s the great thing about math. And computers.
And Kozmic, what the hell is your point of debate here? Seriously, are you just having us on?
Here are the counterexamples.
3 - 3 = 0
π - π = 0
x + x = y + z
3 + 3 = 2 + 4
y and z cannot be 3
x + x = y + z
π + π = ___ + ___
y and z cannot be π
At this point, it seems simplest to keep things in the standard reals. And even in the extended reals, ∞ is not a “number” in the same sense that the other elements are.
Kozmik, do you actually have a point? Can you summarize it in plain English?
x + x = y + z
3 + 3 = 2 + 4
y and z cannot be 3
x + x = y + z
π + π = 6 + ___
z cannot be π
π - π = 0
My point:
The real numbers 3, 2, 4, 6, and 0 are precise.
The real number that solves π + π = 6 + ___ can never be precise.
Horseshit, it’s can’t be.
The missing term–the real number you’re seeking–is n, where n = (2π-6).
It is a real number.
Why on earth does it shock you that an irrational number–2π–cannot be expressed as the sum of two integers? That’s just silly.
Kozmik, this thread is proof that you have no knowledge of maths.
Base 3 will work for that number, but not others. And yes, I have heard of math packages operating on fractions. But even these will not be able to represent all numbers.
You might even be able to represent e as a series - you’ll never terminate the calculation, but it might be possible to have a window of the fractional part you would have to represent.
I am slow to anger, but I’ve had enough. All of you who have been so admirably restraining yourselves, join me here.
This has real life applications. Votes for officers of the MIT Science Fiction Society can be cast for as many candidates as you wish, but have to add up to 1. Negative numbers are not allowed, but irrational numbers are welcome. Typical vote tallies contain several fractions of e and pi and often even more obscure ones.
Kozmik, this is all leading up to the time cube hypothesis isn’t it?
That one’s pretty good. It ruffles my feathers even more that 0[sup]0[/sup] = 1
:smack:
This cracked me up. 
Can you believe I was actually relieved when he unveiled his “infinity hypothesis?” My first thought was, “Thank God he’s not talking about phi.”
…although phi is also an irrational, I just realized.
oooooooooWEEEEEEEEEEEEEEoooooooooooooooo
When Kozmik come back, for the love of God, do not bring phi.
No, it’s a real number. Specifically, one that never terminates.
0.28318531…
Yes.
This has nothing to do with that. This has EVERYTHING to do with the fact that π never terminates and the answer, 0 does terminate.
π - π = 0
So?
No, zero DOESN’T terminate!
You just gave 1 significant figure, 0.
The real value for zero is 0.000000000000000000000000000000000…
Zero never terminates. How do you know that you aren’t really dealing with 0.0000000000000001 unless you do your calculation out to infinite decimal places? You can never write 0 out fully.