Yes; the joke I was going for was that decimal one half would be written as 0.1 bar when converted to ternary. And then multiplying that value by 2 gives you 0.2 bar. Which is equal to ternary 1, in the same way that decimal 0.9 bar equals 1.
I find it really fascinating that different numeric bases all suffer from this same issue, but for different values. That the division by three which breaks decimal representation survives in ternary, but the division by two which is fine in decimal breaks ternary.
Of course, it seems to me that the real underlying problem is that we insist on writing these values out as an infinite series of fractional digits in the first place, instead of keeping the values in a precise fraction form. One third times three equals one; there’s no controversy there even in decimal. It’s only when someone insists on actually performing the division and representing that initial “one third” value as being a zero followed by an infinite number of fractional threes that the whole “omg 0.9 bar equals one??” paradox appears.
I find it really fascinating that different numeric bases all suffer from this same issue, but for different values. That the division by three which breaks decimal representation survives in ternary, but the division by two which is fine in decimal breaks ternary.
Of course, it seems to me that the real underlying problem is that we insist on writing these values out as an infinite series of fractional digits in the first place, instead of keeping the values in a precise fraction form. One third times three equals one; there’s no controversy there even in decimal. It’s only when someone insists on actually performing the division and representing that initial “one third” value as being a zero followed by an infinite number of fractional threes that the whole “omg 0.9 bar equals one??” paradox appears.