Is there any reference book from which I can learn the basic usages applied to the proofs in mathematics? I met several problems these days, for instance, "两者不能同时成立" seems hard for me. Thank you!
are you looking for "contradictory", in mathematic, it would be:
"contradictory opposite" "矛盾否定"
"contradictory propositions" "矛盾命題"
教育研究院, of taiwan has documentations of bilingual academic terms, the mathematical one is here, you may download it:
I guess your mean you are writing math proofs and want to say something like "A holds, or B holds, but not both".
I seldom write proofs in Chinese nor am I a math student, but I do read a little bit math written in Chinese.
I think "A成立，或B成立，但非同時" is perfectly fine and clear.
However, if you do want to be academic, then the translation for Exclusive Or in Mathematics is "異或". So you can say "A異或B". But I doubt how many people understand except the math guys.
If what you mean is not "are not both true" but "cannot both be true", or "mutually exclusive", then "互斥" suggested in another answer sounds like the correct choice.
If I have two conditions, ONLY one can be true.
Either A or B is true. We cannot make two conditions (both A & B) become true.