1/3 + 1/3 + 1/3 = 1
1/3 = .333R
.333R + .333R + .333R = .999R
therefore .999R = 1
Precisely and exactly equal.
Yeah I figured that one out for myself. But it still feels wrong don't it?
As a non-mathematician, the above explanation is interesting as it seems to indicate something I'd never considered: that the decimal system is not always adequate (or, indeed, 100% accurate). Expressing 3 thirds as equalling one is perfectly expressed by the use of fractions (1/3 + 1/3 + 1/3) but is not perfectly expressed by the recurring decimals. I guess that's why it feels intuitively wrong.
The fact that you have to state that the decimal numbers are recurring is an indication in itself that it's an inadequate system because you can never perfectly express a third in decimals, unless I suppose you are using base 3, or a multiple thereof, but then you'll have problems expressing other fractions.
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