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1 Divided by 2 = more than 2 halves?

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If you have 1 and nothing else at all, divide this in half, you have 2 halves but have also in the process formed a third state which is in-between or now contains both halves?

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You've rediscovered the Pythagorean doctrine of number (from about 500BC). First there is nothing, but it is only one nothing, so there is one. And the nothing together with the one make two. And the two together with the one make three...

You've re-stated it by saying that at first there was one and nothing else, which gave you a two and hence the possibility of halving. But you don't define "between". For the Pythagoreans the sequence is purely consecutive because of the way it's produced.

A more modern and mathematically rigorous version of the idea (which sorts out the problem of ordering) is the successor function.


Edited by acey

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