Wednesday, October 25, 2006

It's stuff like this that makes my brain squirm

Wikipedia's entry on 0.999... (a repeating decimal that goes on for infinity). Read the first sentence:
In mathematics, 0.999... [can't reproduce the symbols here] is a recurring decimal exactly equal to 1.

Now, if you're like me (and probably 99% of the rest of humanity), you look at the number 0.999... and think, "That's not exactly equal to 1 because it's not 1!" Your eyes are telling you it's not exactly equal to 1.

Now scroll down the Wiki page to the proofs and look at the little grey boxes on the right. This is where the squirming begins.

First, the fraction proof in my words. We all know that three thirds (or as we Norwegians say, "tree turds") equals exactly 1. Well, one third ("one turd") equals 0.333... (another infinitely repeating decimal), so 0.333... + 0.333... + 0.333... = 0.999... or 1.

Or how about the algebra proof? I'll just leave this one to speak for itself:

c = 0.999...
10c = 9.999...
10c − c = 9.999... − 0.999...
9c = 9
c = 1

This stuff makes me glad that the most amount of math I usually have to do involves balancing a checkbook to two decimal places.


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