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RE: I will bite, a defense of sorts
I'd also like to add that the concept of faith shouldn't seem that odd, even to the atheist. Faith is an essential part of any action, as perfect knowledge is beyond the grasp of everyone. Of course, there are statistical principles (such as Bayes' Theorem) that outline ways to take a best guess at what is likely and not so likely, but these do not limit the choices to what is scientific. Specifically, there are many instances in which determining what is probable relies wholly on unscientific things like "feelings."
Feelings are not statistical data; when confronting guesses about the future, your feelings typically result from application of your knowledge of how past events made you feel applied to the present. They are more of a factor in utility calculations than in determining probability. I might be hesitant to do something highly improbable if it resulted in very unpleasant feelings, which is not actually a commentary on probability but on my risk assessment criteria.
Then again, principles of science aren't necessarily excluded from religious decision making. Alma 32 in the Book of Mormon contains a great analogy of the process of an idea becoming knowledge and how faith is integral in that conversion.
Does the LDS religion view ethics as teleological or deontological?
RE: I will bite, a defense of sorts
Actually, 1 = 0.999.... It is not an approximate statement. Hard to grasp, yes, but no approximations have been made. It is easier to look at 0.111... first, it is simpler to deal with. To get, 0.999..., you just have to multiply the result by 9.
Now, 0.111... is really the series 0.1 (1 + 0.11 + 0.12 + ...) which is a geometric series. In generic terms, a geometric series is written a + ar + ar2 + ..., and in our case a = r = 0.1. For a finite number of terms, n, it is relatively easy to show that the sum of the series is simply
a (1 - rn + 1) / (1 - r).
For an n number of terms of the series 0.111..., the sum would reduce to
(10n + 1 - 1)/(9 10n + 1),
with the result of 11/100, 111/1000, 1111/10000, ... for n=1,2,3, ...
When n is allowed to grow large, i.e. approaches infinity, this sum will converge iff r < 1. To determine what it converges to, break the fraction in the generic formula into two pieces: one with a as its numerator, and the second with a*rn + 1 as its numerator. Only the second piece depends on n at all, and it approaches 0 as n approaches infinity. Since, the first piece does not depend on n, it will remain constant as n approaches infinity. Hence, the infinit series will converge to
a / (1 - r).
For a = r = 0.1, the resulting sum is just 1/9, which we have just shown is equivalent to 0.111.... From this you can see directly that 1 = 0.999... = 1.000..., implying that decimal expansions are not unique. While they still may not be comfortable ideas, the concepts of limits and convergence are well founded. It just took until Newton and Leibniz to make the leap necessary, solidifying the ideas.
I encourage you to look over the proof for sum of the finite series, as it is a very clever technique that should be in any mathematician's tool box.
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RE: I will bite, a defense of sorts
You beat me to the punch, but did an excellent job, so I can't complain.
Another good example to add to your list of things not logical is the ability to mathematically prove that .999... = 1:
Sure, they are approximately the same, but they aren't supposed to be equal. So much for pythagoreanism.
I'd also like to add that the concept of faith shouldn't seem that odd, even to the atheist. Faith is an essential part of any action, as perfect knowledge is beyond the grasp of everyone. Of course, there are statistical principles (such as Bayes' Theorem) that outline ways to take a best guess at what is likely and not so likely, but these do not limit the choices to what is scientific. Specifically, there are many instances in which determining what is probable relies wholly on unscientific things like "feelings."
Then again, principles of science aren't necessarily excluded from religious decision making. Alma 32 in the Book of Mormon contains a great analogy of the process of an idea becoming knowledge and how faith is integral in that conversion.
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