Quote:
Originally Posted by TurboFan
I see the difference in logic. You're theorists, I'm an engineer. Nothing wrong with either, just a different approach!  |
Well, theorists probably isn't the right descriptor...
Everyone (I'm generalizing) knows:
1/3 = 0.333... (where "..." represents an infinitely repeating sequence)
That's simple enough, right? Lets multiply it by three!
3 x 0.333... = 0.999...
Well, that makes sense, doesn't it? So how about this?
3/3 = ?
You just did the math, didn't you? Three thirds is equal to 0.999...! How can that possibly be?
Basically it boils down to the concept of an infinite number, and the fact that two numbers are considered identical if (and ONLY if) their difference is equal to zero. Given any positive value, the difference between 1 and 0.999... is less than this value (this can be demonstrated using some complex maths that I'm not interested in posting). Thus the difference is 0 and the numbers are identical.
This is such a trivial anomaly that it's widely accepted that any mathematical procedure ending in 0.999... is considered to be 1. (This last bit is just my interpretation, and quite possibly over-simplified and incorrect. Take it with a grain of salt.)