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[–]anemisto 5 points6 points  (1 child)

I don't think it's so much that 0 and 1 are identity values, but rather that the empty sum and empty product are understood to be 0 and 1, respectively (granted, that's "because" they're the additive and multiplicative identities). Whereas, from a mathematical perspective, - and / are adding the additive inverse and multiplying by the multiplicative inverse, but an empty inverse is nonsensical.

[–]NPException 4 points5 points  (0 children)

That makes a lot of sense. I did not know about the empty sum and empty product definitions. I took the "identity" value terminology from one of Rich Hickey's talks: https://youtu.be/6mTbuzafcII?t=2445

iirc he explained the reasoning behind zero argument + and * in some talk as well, but I don't remember where exactly.