Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

The question asks if there can be a relation on a set that is neither reflexive or irreflexive. The example the book give makes perfect sense: "Yes, for instance $\{(1,1)\}$ on $\{1,2\}$."

I was wondering, if I had the relation on that same set $\{1,2\}$, would that be irreflexive?

share|improve this question
Yes. In fact, the relation $\{\langle 1,2\rangle\}$ is irreflexive on every set that contains both $1$ and $2$: it contains no ordered pairs of the form $\langle x,x\rangle$. –  Brian M. Scott Nov 3 '12 at 17:14
Thank you very much. That was an insightful response. –  Mack Nov 3 '12 at 17:22
You’re very welcome. –  Brian M. Scott Nov 3 '12 at 17:23
This question appears to be off-topic because it is essentially a yes-or-no question with no conceivable future value. –  Lord_Farin Dec 25 '14 at 22:11
@k170, did you really consider that bit of MathJax was enough justification to bump this very narrowly scoped, two-year-old post I was trying to purge from the system? Please look at the last active date before editing. –  Lord_Farin Dec 25 '14 at 22:42

Your Answer


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

Browse other questions tagged or ask your own question.