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Definition of Reflexivity (Wikipedia):

In mathematics, a binary relation R over a set X is reflexive if it relates every element of X to itself. ∀x ∈ X : x R x

It can reflexive since it could be $a=b$ ($a,b\in\mathbb{R}$) But it could also be irreflexive: Since it doesn't have to be equal.

Should I think like this: $a\leq b$ is reflexive since we got the relation $\leq$, which implies it doesn't have to be equal but until we don't know the results it's reflexive.

Kinda not the smartest question, but I'm fairly interested into the thought process of yours :)

*pardon for my bad English, I'll look to improve it further.

Mittens
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ShareholderOfVoestalpine
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    A relation is reflexive if $a\sim a$ for all $a$ in the set. Since $a≤a$, this relation is reflexive. – lulu Aug 28 '20 at 22:47
  • You also need to specify which set $\leq$ is meant to be a relation on (not that this will affect the answer very much, but if you don't your question is not fully specified). – diracdeltafunk Aug 28 '20 at 22:47
  • The relation is $\le$, not $a \le b$. It is a two place function. It takes two arguments and returns true or false depending on the arguments. – Ross Millikan Aug 28 '20 at 22:53
  • Thank you guys for the answers, all of them were helpful. I'll next time always put the definition on the question. – ShareholderOfVoestalpine Aug 28 '20 at 22:59

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A relation $R$ on $A$ is reflexive if $(a,a)\in R$ for all $a\in A$.

In particular, the relation $aRb$ iff $a\leq b$ (either $a<b$ or $a=b$) on an totally ordered set $(A,<)$ is reflexive since $a\leq a$ for all $a\in A$.

Mittens
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