What is the equivalent of reciprocal but for the sum instead of the product?

Question

Reciprocal is defined as:

Two expressions or functions so related to another that their product is unity

So if $$\alpha * \beta = 1$$

Then you can say $\beta$ is the reciprocal of $\alpha$ i.e. $\beta = \dfrac{1}{\alpha}$

If $$\alpha + \beta = 1$$

is it possible to say $\beta$ is the _ ? _ of $\alpha$ ?

* Edit *

This question is in the context of probabilities. For example if $\alpha$ is the probability of event X occurring and $\beta$ is the probability of event X not occurring.

Note: $0-\alpha=\beta$ means $\beta$ is the opposite of $\alpha$ — J. W. Tanner, Aug 10 '20 at 21:15
We use $1$ in the reciprocal because $1$ is the multiplicative identity. We should use $0$ in the opposite because $0$ is the additive identity. — Brian Tung, Aug 10 '20 at 21:17
Thanks @BrianTung this was in the context of probabilities. I was wondering if there was a term for this relationship. I'll update the question to include that. — AJP, Aug 18 '20 at 07:39
Possibly relevant: https://math.stackexchange.com/questions/2425698/1-minus-percentage-what-is-this-called — Brian Tung, Aug 18 '20 at 07:45
Thank you @BrianTung. Perfect, it's called the Complement. I'll mark this as a duplicate. — AJP, Aug 18 '20 at 07:47

score 3 · Answer 1 · answered Aug 10 '20 at 21:15

3

"Negative of" or "additive inverse of", or "opposite of" as suggested in comments.

answered Aug 10 '20 at 21:15

Ethan Bolker

103,433

Right, I grew up calling it the “negative”, but then I’m even older than you. – Lubin Aug 10 '20 at 21:20
I think "opposite" is used like this only in the early years of schooling. – GEdgar Aug 10 '20 at 21:22
@Lubin Not by much, and less and less in proportional terms each year. – Ethan Bolker Aug 10 '20 at 21:22
What about 'negation'? – Oscar Cunningham Aug 21 '20 at 12:53
@OscarCunningham You could, and be understood. I wouldn't - "negation" usually applies to logical propositions. – Ethan Bolker Aug 21 '20 at 14:20

What is the equivalent of reciprocal but for the sum instead of the product?

1 Answers1