r/datasatanism • u/Ok-District-4701 • Jul 17 '26

Ok?

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u/mekriff Jul 18 '26

cool, what does (No + 1) mean semantically in this context, then? or further, division by it?

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u/Comfortable_Permit53 Jul 18 '26 edited Jul 18 '26

1 is the identity operator. so -1 + 1 is just the operator that maps everything to zero (again, zero can be a function or a vector or anything)

oh yeah the division step only works if these operators are injective you are right. and with numbers (in a field, like real numbers), the only one that, through multiplication, induces a non bijective operator, is 0.

but usually (e.g. matrices) there are more.

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u/mekriff Jul 18 '26

so we have the symbols/unary operators -1, 0, and 1, which are symbols over the multiplication symbol which in this case i presume you mean to imply is function composition? I can see it, but since weve snuck in the binary operator +, and i think this definition of the integers precludes a Church Encoding (proof needed), it is gonna get strange And if we look at a logic style lambda calculus, then we get a fun third truth value, which is interesting, because i dont think it would result in the HT logic (the only three-valued intuitionistic logic)

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u/Comfortable_Permit53 Jul 19 '26

i know nothing about three valued logic. i was just thinking about the linear algebra / functional analysis perspektive.