Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

What are functions applied to either side of a relation that maintain the relation called? What are these kinds of processes/functions/operations called? What are the functions that violate the relation called?

Edit : removing the comment about equality relation.

share|cite|improve this question
If you have an equivalence relation $\sim$, a function or operator $f$ is said to "be well defined modulo $\sim$" if $x\sim y$ implies $f(x)\sim f(y)$. Equality is a particularly bad example because every function or process must respect =. – Arturo Magidin Jun 12 '11 at 4:01
Please try to make your posts self-contained; the question should be posed in the body, and you should not relay on the title to begin your presentation. – Arturo Magidin Jun 12 '11 at 4:02
up vote 3 down vote accepted

I think it would be acceptable and within convention to say the function is "relation-preserving" because the relation still holds true under the action of the function, i.e. $x \sim y \implies f(x) \sim f(y) $.

Mathematicians often speak of certain properties or even equations being preserved under maps and transformations, so this choice of term has support.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.