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Is there a name for numbers which, for a particular calculation operator, don't change the result?

E.g. while adding, $0$ does not affect the result, which is also why we choose it as the starting point for a sum. When multiplying, $1$ does not change the result, which is also why we choose it as a starting point for factorials.

I'd like to know more about these sort of numbers, but it's hard to google for them not knowing their name.

Thomas Weller
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    They are the identities for the operation in question. – Ross Millikan Jan 08 '20 at 15:43
  • Several "numbers" don't change the result. $0$ for addition $1$ for multiplication, $id$ for composition of maps, etc. Can you be a bit more precise what kind of operator you have in mind? – Dietrich Burde Jan 08 '20 at 15:43
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    https://en.wikipedia.org/wiki/Identity_element –  Jan 08 '20 at 15:45
  • What I usually do is I going to wikipedia in my language and then clicking the links to the same page in other languages. –  Jan 08 '20 at 15:46
  • @Gae.S.: thanks. I didn't even know it in my native language :-) – Thomas Weller Jan 08 '20 at 15:48
  • I was tempted to delete this question. If you agree, I'll leave the question here, because there are no good Google search results for the sentence in the title. @Gae.S.: Identity element is exactly what I was looking for. Do you want to post it as an answer? – Thomas Weller Jan 08 '20 at 15:55
  • I think J.G.'s answer is fine. –  Jan 08 '20 at 16:22

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I'll just add two things to the observation in comments that the term "identity" [Wikipedia] is sought. Firstly, for non-commutative operations we must distinguish between left- and right-identities. Secondly, and this is something of a tangent: the very different property $0$ has in multiplication, viz. $0x=0$, earns it the name absorbing element. And $1$ is an identity for exponentiation on one side and an absorber on the other.

Thomas Weller
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J.G.
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