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Is there a term for the relationship between some number and a number added to it that makes it equal one? i.e. $x + y = 1$, thus $y$ is the _________ of $x$.

In the case I'm looking at, the numbers are the cross-ratio of $\left ( z_{0},z_{1},z_{2},z_{3} \right )$ rearranged. So if I switch $z_{1}, z_{2}$, the resulting cross-ratio when added to the original cross-ratio gives me 1. I feel like I should be able to call that something...

Silvia Ghinassi
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Jenjenjude
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  • Oh, this is a very interesting question. Yes, there is a word that is specifically for that. I remember seeing it when I was a kid, in some very old book. I would like to read about it again. – OR. Jul 22 '13 at 16:33
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    Perhaps "complement" would work (from probability)? – Adriano Jul 22 '13 at 16:49
  • $ax+by=1$ is a linear diophantine equation, possibly this is what you are thinking of? – zzzzzzzzzzz Jul 22 '13 at 17:24
  • @Adriano, I think that just invites confusion—the complement of an event in probability theory is a special case of the complement of a set in set theory, which is a special case of the complement of an element in lattice theory. This usage doesn't match those general notions whatsoever. – dfeuer Jul 22 '13 at 19:01
  • I had been trying hard to remember. All I could remember was: Aliquot: an exact divisor of a quantity, supplementary angles: angles adding up to $180$, complementary angles: angles adding up to $90$. But then I remembered I saw the thing in an old mathematical tables book. This got me to the image I was looking for: $1-\sin(x)$. What I remembered was not exactly $1-x$ but the funny name for the trigonometric functions $1-\sin(x)$ and $1-\cos(x)$. (http://en.wiktionary.org/wiki/coversed_sine). – OR. Jul 22 '13 at 19:32
  • Hmmm...thanks for the ideas! I decided to just write it in terms of x, essentially, to avoid having to call it something--though I still believe that term MUST exist! :O) I'll look up linear diophantine equation--that might be close. Does anything spring to mind if I mention I'm looking at the 6 values of the cross ratio? (http://en.wikipedia.org/wiki/Cross_ratio) under "Action of symmetric group"... – Jenjenjude Jul 22 '13 at 20:17

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