Exercise 273Logic, sets and proofs › RelationsHigh schoolAdded 3 Nov 2026

Reflexive relations

#reflexive#relation#definition

Statement

Define a reflexive relation and determine whether $a\mathcal{R}b\iff a<b$ on $\mathbb{R}$ is reflexive.

Hint

Reflexive means $a\mathcal{R}a$ for all $a$ .

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Definition. $\mathcal{R}$ on $A$ is reflexive if $\forall a\in A$ , $a\mathcal{R}a$ .

Test. For $a\in\mathbb{R}$ , $a<a$ is false, so $a\mathcal{R}a$ never holds. Not reflexive.

Conclusion. The strict order $<$ is not reflexive.