A few months ago I came across a paper about how rational numbers can be represented as LEFT-infinite digit sequences without a decimal point.
For example, in base ten,
−1 = ...9999
because adding 1 to it gives ...0000. Similarly,
1/3 = ...6667
because multiplying it by 3 gives ...0001. It's a fun exercise to verify that 1/3 − 1 = −2/3 indeed holds in this system.
I can't find this paper any more. Does anyone know what it might be?
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