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.999999... == 1? (Somewhat OT)by Sherlock (Deacon)
|on Jul 25, 2001 at 00:37 UTC||Need Help??|
This post is somewhat off topic, but I've begun to notice that there are enough math buffs around here that some of you may get some enjoyment out of this (if you haven't seen this already, that is).
A math professor of mine came to me one day with a proof. Although I can't remember the exact format, I can recall the general concept. This proof stated that .9 repeating was equal to the number 1. Following are the arguments to support this statement:
1. By Substitution
3*(1/3) = 1
1/3 = .3 repeating, therefore
3*(.3 repeating) = 1
However, 3 * .3 repeating = .9 repeating
Therefore, .9 repeating must be equal to 1
2. By the Interval Between Numbers
It is give that, for any two distinct numbers, there is an infinite number of values that fall between the two. For example, between 2 and 3, there is an infinite number of values that are greater than 2 and yet less that 3.
If that's the case for all distinct numbers, give me just one number that falls between .9 repeating and 1 (after all, if they're distinct, there should be an infinite number of values between them - I only ask for one, as that would disprove the above statement).
For a long time, I found this argument impossible to refute. One day, while in the shower, no less, I think I came upon a reasonable argument against this statement. Of course, I, unlike the professor that proposed this to me, do not have a PhD in mathematics and I'm sure my proof could be somewhat more sound.
Rather than simply giving what I consider a "fairly legitimate" answer, I'd like to see what arguments I can get from the other monks either supporting or refuting the above statement. I'm really looking forward to seeing what types of arguments I see. Assuming that the rest of the monks don't give my answer verbatim, I'll post my answer in a day or so and you can all have fun ripping it apart.
Have a little fun. Good luck!
Skepticism is the source of knowledge as much as knowledge is the source of skepticism.