Question

what type of a relation is less than in the set of real numbers

Answer 1

reflexive relation .....

Answer 2

Its not reflexive. In fact x < x is false for all x ∈ R, thus it is irreflexive.

Its anti-symmetric but not in usual way. The statement of anti-symmetry is

R( a, b) ∧ R(b, a) ⇒ b = a, for relation R. But, for <, the LHS is never true

ie, a < b ∧ b < a is always false. Thus statement of anti-symmetry is true, because if A is false then A ⇒ B is trivially true.

Irreflexible and anti-symmetric is then termed as asymmetric.