Post
by Timm001 » Tue May 21, 2013 1:14 am
Paidion,
Thank you for expanding upon your explanation. I think that my concerns may have been stated in a way that was less than fully articulate. I see now that what I am thinking is that there might be one of two problems going on with your proof: 1) Either it does not in fact prove that 0.999… = 1 because it is simply a demonstration of how we use mathematical conventions, or 2) It contains a false statement, in which case it is simply invalid.
Let's start with the second of these concerns because it is easier to show and leads naturally to the first. As such, we can begin by looking at the third line of your proof:
9n = 9.000…
My point here is simply that this is a false statement. I will readily admit, however, that my training in mathematics is limited. I finished calculus in high school and I hadn't studied it again until I took the GRE. What I do think that I know, however, is that something is wrong with your equation if it generates a false statement. I think that this line is a false statement. My reasoning is as such:
1. n = 0.999… (stipulation)
2. 9n = 9.000… (third line of your proof)
3. 8.999… = 9.000… (consequence of 1 and 2)
Now perhaps it is the case that, per my second concern, certain non-terminating decimals are taken to be equivalent to certain appropriate integers (rounding up) via the conventions of mathematics which we have all been taught in grade school. So 1.999… is equivalent to 2, and 2.999…is equivalent to 3, and so on. However, if this is much is true, then I think that what you have offered is less of a "proof" than a demonstration of mathematical convention. I, for my own part, tend to believe that numbers exist and are real, abstract objects, therefore the number 8.999… is not equivalent to 9.000…, even if our mathematical conventions treat them as one and the same because any such distinctions hold no particular relevance to our typical mathematical interests. I am not sure how this principle applies, however, when dealing with negative numbers such as -0.999…, in which case we cannot "round up" to -1.0...
So it is possible that what you have shown is that mathematicians have agreed to do math in a way where they treat .999…as equivalent to the integer 1. I am not sure of what precisely count as a "proof" in mathematics, but, from what I can tell, your "proof" does not work unless you assume that 1.999..is equal to 2, and that 2.999 is equal to 3, and so on. Therefore, if you must assume it, then it is not a proof. Further, it will not work as proof to convince me that the number 8.999…, as an abstract object, is equal to 9.000... However, it is possible that simply demonstrating appropriately how the axioms of a mathematical system work is sufficient to count as a proof, in which case I cannot fault your conclusions.
However, perhaps we can find common ground in the thought that these kinds of agreements ought not to be taken as the best guide to the nature of reality. Such arrangements may work for the time being but turn out to be fallacious when someone presents a counter-proof, or they simply might not apply to reality at all. The fact that you had to employ a non-standard method of subtraction in order to subtract .999… from 9.000… seems slightly ad hoc, though I cannot object that it is an unacceptable mathematical practice.
But for the purposes of making a claims about individual salvation, I would suggest that we do not read too much into mathematical conventions when drawing conclusions about the nature of free will and repentance. We may agree that .999…is equal to 1 and get on with our math, but this does not mean that it is true nor that it has corollaries to reality.
