how to call a and b when a+b=1?

Question

I guess it's a simple question, but it really escaped my memory.

If $a + b =1$, then how can I call those $a$ and $b$ numbers?

$a$ is not an inversion of $b$, and it's not reciprocal of $b$.. but I'm sure that they do have a 'name'.

Answer 1

Grammatically, it would make sense to say that $a$ is the unit complement or unity complement of $b$. Google attests that this phrase is occasionally used, but I wouldn't call it common.

Answer 2

This pair of numbers has no special name in mathematics as I know. Because usually mathematicians use $\lambda$ and $1-\lambda$ instead of $a$ and $b$ and there is no need to use a special name...

Answer 3

I've considered posting this as just a comment, because I am quite sure, this does not really answer the question (but is a bit related). But since I tend to write more, I've chosen to post an answer.

Background

Consider $V$ a vector space over the field $\mathbb{K}$ (e.g. $\mathbb{K} = \mathbb{C}$ and $V = \mathbb{C}^n, n \in \mathbb{N}$). Then there is well know term linear combination of vectors. If $\alpha_i \in \mathbb{K}, v_i\in V, i = 1, \ldots, n$, then linear combination is the expression

$$ \sum_{i=1}^n \alpha_i v_i = a_1 v_1 + a_2 v_2 + \ldots + a_n v_n $$ when the vectors stand alone. Or for some $x\in V$ we say, that $x$ is linear combination of $v_i$ if

$$ x= \sum_{i=1}^n \alpha_i v_i. $$

Answer

Now, to the question. Beside linear combination, there is somehow sub-term of linear combination called affine combination. We again have $\alpha_i \in \mathbb{K}, v_i \in V$. And we say, that this

$$ \tag{1} \sum_{i=1}^n \alpha_i v_i $$

is affine combination, if additional combination holds, which is

$$ \tag{2} \sum_{i=1}^n \alpha_i = 1. $$

So, there is not really a name for those $\alpha_i$ (maybe just affine coefficients), but the expression (1) is called affine combination (of $v_i$) if the condition (2) holds.

In your case $a, b$ might be those affine coefficients for some vectors in general.