staving Alex Fink:
> Anyway, there are conceivable base-type systems where it's worse. For
> example (I think), consider the base-3 system where the digits are 0, 1, and
> -7, which I'll denote s. Counting then runs
> 0, 1, 10s, 10, 11, 11s, 10s0, 10s1, 11ss, 100, 101, 10s0s, 110, 111, 10s1s,
> 11s0, 11s1, 11sss, 10s00, 10s01, 100s, 10s10, 10s11, 101s, 11ss0, 11ss1,
> 10s0ss, 1000, ...
>
I used to play around with a base 1+i counting system at one point.
Digits could be 0, 1 or i
Base i+1 Decimal
0 0
1 1
i i
10 1+i
11 2+i
1i 1+2i
i0 i-1
i1 i
ii 2i-1
100 -2
101 -1
10i -2+1
110 i-1
111 i
11i 2i-1
1i0 i-3
1i1 i-2
1ii 2i-3
i00 -2i
i01 1-2i
i0i -i
i10 1-i
i11 2-i
i1i 1
ii0 i-3
ii1 i-2
iii 2i-3
This base is mainly of interest to particularly insane mathematicians.
Pete
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