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Question:

Is there a way to definitionally describe rational numbers $a$ and $b$ when $a+b=1$?

Answer:

My guess is that $a$ and $b$ may be defined as `unitary additive complements,' but this is just a guess.

MJD
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Michael Levy
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  • Formulas were invented to avoid such linguistic abominations, imho. What's wrong with $a+b=1$? –  Jul 09 '17 at 17:08
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    The word "complement" is reasonable, especially if they are between $0$ and $1$, but it's not exactly a standard term, except maybe in the context of talking about probabilities, where this would naturally be of interest. – G Tony Jacobs Jul 09 '17 at 17:08
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    I would tend to just refer to $b$ as "$1-a$" – G Tony Jacobs Jul 09 '17 at 17:09

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In the same way that the error function, erf($x$), and the complementary error function, erfc($x$), sum to one (i.e., erf($x$) + erfc($x$) = 1) [1], so too then are $a$ and $b$ complementary under addition if $a + b = 1$.

[1]

https://en.wikipedia.org/wiki/Error_function#Complementary_error_function

Michael Levy
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