property holds for all bases except 2

Question

For any base $n$, for $n > 2$ the following holds:

$1/(n-1) = 0.111...$

However in base 2 this doesn't hold. It's just 1. It's obvious why that is you have $1/1$, but I always get uneasy with non-0 and non-1 exceptions in an otherwise flawless rule. Is there any way to shed some light on this?

What's the rule for $1/(n-(n-1))$? Which rule wins at $n=2$? — Eric Towers, Apr 29 '14 at 20:50
@EricTowers I don't get it, $n/(n−(n−1))$ is just $n$ right? — Cruncher, Apr 29 '14 at 20:54

score 2 · Accepted Answer · answered Apr 29 '14 at 20:51

2

The equation also holds in base $2$. Note that that claim is the same as the $0.9999\ldots=1$ in the world of ten-finger people.

answered Apr 29 '14 at 20:51

Hagen von Eitzen

374,180

property holds for all bases except 2

1 Answers1