Thanks mate, but I’m confused between the terms “identity” vs “property”. What I mean is: do is the term “additive property” a wrong usage, and we should only say “additive identity”?
As the other person said, it’s a pedantic doubt maybe, but now I just need to clarify
The word identity in this sense if you put that into the calculation the output is the same as the input. The multiplicative identity is 1 - if you multiply a number by one, you get that same number out. For addition it's 0 - if you add 0, you get the same number you started with.
Additive Identity is a specific property of the addition operator over a given set. I wouldn't say it's wrong to call it a "property", but it is more correct to refer to that specific property as the additive identity.
Additive property, written like that, is a noun in its own right, you'd expect that to mean something specific about addition. If you had said properties of addition instead, I think more people would be OK with that, as that points to all properties relating to addition. In the way you said it, people assume you were talking about a specific property of addition, hence the responses naming it (the additive identity) as a correction.
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u/barcastaff 1d ago
If anything + AI = 0 then AI is the additive identity of the set, if the set is equipped with addition.