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In French when you have an expression of the type $\sqrt{x}-\sqrt{y}$, the expression $\sqrt{x}+\sqrt{y}$ is named the "quantité conjuguée". This is useful when you want to bound $$\vert \sqrt{x}-\sqrt{y} \vert = \frac{\vert x-y \vert}{\sqrt{x}+\sqrt{y} }$$

What is the equivalent wording in English?

By the way second question... when I use the word "expression" above, is it appropriate? Would "quantity" be better?

wythagoras
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mathcounterexamples.net
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1 Answers1

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In English, it is also termed the "conjugate." The conjugate of $a+b$ is $a-b$.

As for your second question, "expression" is better (in the sense that it has a firmer meaning), though "quantity" also works.

Peter Woolfitt
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  • Easy... thanks Peter. And is "expression" appropriate to refer to something like $\sqrt{x}-\sqrt{y}$ – mathcounterexamples.net Jun 07 '15 at 09:18
  • @Jean-PierreMerx I have just updated my answer :) – Peter Woolfitt Jun 07 '15 at 09:22
  • It makes no sense in general to say that $,a-b,$ is the conjugate of $,a+b,$ (else e.g. $,0=0+0,$ has conjugate $,0-0,$ contra $,0 = 1-1,$ has conjugate $,1+1).,$ Conjugation is well-defined only in specific contexts (as in the OP, the conjugation automorphism of a quadratic field). – Bill Dubuque Jun 07 '15 at 18:30
  • I think it makes sense for the conjugation of "$a-b$" to be "$a+b$," but only if we keep it in the form of just exchanging plus/minus between two quantities. – Peter Woolfitt Jun 09 '15 at 05:17