What are you, Ecmandu now? A universally accepted conclusion of middle-school level arithmetic is ‘my premise’ to be compared on equal ground to whatever the fuck is bouncing around in your head?
No, One divided by three = .333… is not ‘my premise’. If you don’t accept basic math, I can certainly understand why you wouldn’t think .999… = 1. There’s probably all sorts of basic shit you get wrong if you don’t know how fractions work. But how does that affect me? My argument is based on universally accepted arithemetic, your argument is based on some shit you made up- I feel zero burden of proof. In the absense of any argument from you.
unacceptable as a premise[/b] for the reasons that I have given.
One divided by three = .333… is an unacceptable premise? You think you have reasons why simple division is inadmissable in a conversation about math?
So if you want to do anything other than be rejected,
That’s an impossible scenario. If you’re willing to casually dismiss 6th-grade level short division to defend your premise, you will dismiss literally anything and everything that doesn’t fit your conclusion. It’s obvious that the only way I could not be rejected by you is to agree with you.
you need to drop that premise and come up with one to which we can both agree.
See above. If “What’s one divided by three?” is controversial to you, you don’t belong in a conversation about math. I have no interest in trying to find ‘a premise we can both agree on’ with somebody who is already rejecting arithmetic. How could I possibly do that anyway? If you don’t know what one divided by three is, do you know that ice is frozen water? Do you know that A +B = B + A? How can anybody possibly be expected to meet the standard of ‘providing premises James can agree on’ when james can’t agree on the conclusion of dividing one digit numbers?
And also, as also stated repeatedly, as long as you merely attempt to provide a proof in your preferred direction without finding the flaw in my proofs, you aren’t actually making progress.
Of course I’ve made progress. I’ve given the reasonable people in the thread additional reasons to accept .999… = 1. I’ve been here too long to have set ‘make James change his mind about something’ as a goal.
I will agree to that as a premise if you wish.
The same procedure that shows 1/2 =.5 shows that 1/3rd equals .333…
If not, what does it equal? 1/3rd is just a magical fraction that can’t be converted to a decimal? 1/3rd doesn’t have a value? People can’t divide things into threes?
The series 0.999… is the result of an operation:
0.999… = 0.9 + 0.09 + 0.009 + 0.0009 + … =
It’s also the result of an operation 3(1/3). That’s the thing about numbers; there’s an infinite number of operations that can have them as a conclusion. What’s the significance in focusing on one when there are others?
That series of operations has no opportunity to become different no matter how long it is carried out.
Wait, is it an operation, or a series of operations? If it’s a series of operations that can never be completed, then nothing is the conclusion of it. It makes no sense to talk about the ‘result’ of an infinite series of operations, that’s incoherent. 3(1/3) isn’t an infinite series of operations, though. And it results in .999… as well. Or 1, if you prefer.
That is why it is “endless” or “infinite”. The result of every operation is that there is required to still be a small percentage between the accumulated result of the operation and 1.0. As long as the operation adds only 90%, there will always be a 10% not added into the accumulated sum. Thus the difference between the sum and 1.0 can never become zero. QED
.999… is not an operation, it is a number. At some point in your proof you confused one for the other. You’re talking about the operation never reaching the sum of one, but we’re not talking about some operation (or infinite series of operations) you chose, we’re talking about a number. And that number can be achieved with operations other than yours.
If I wanted to, I could say that 2 is the result of the operation
1+
.5
+.25
+.125
and so on, adding half of the previous amount, drawing infinitely closer to 2 but never reaching it, and then try to preposterously argue that 2 isn’t a real value. That’s all you’re doing here- picking a preposterous method of allegedly reaching .999… that doesn’t actually reach it, when their are other ways of reaching it, and then trying to conclude something about the nature of .999… on the basis of it.
1.0 – 0.999… = 0.000…1
That is an infinite set of non-zero items.
First of all, according to your past arguments, “0.000…1” isn’t a number, so the difference between 1 and .999… doesn’t have a value, which means they are equal. Second, since numbers can be derived with multiple operations, the fact that one particular one leads to an odd result doesn’t mean much.
3)
0.999 = real number
“…” = infinite, non-real number
[/quote]
.999… isn’t an infinite non-real number, it’s a value equal to one. For the same reason that .222… in ternary is equal to one-half.
4)
1.0 is a “bounded decimal”
0.999… is an “unbounded decimal”.
The same number cannot be both bounded and also unbounded. QED
[/quote]
Of course they can.