Does R (real number line) have linear order?

Question

I'm not sure if R has linear order, I know that it has the property of transitivity and comparability but I'm not sure if it has Nonreflexivity.

Answer 1

$(\mathbb{R}, <)$ is non-reflexive and $(\mathbb{R}, \le)$ is reflexive. When people say something like "$\mathbb{R}$ has a linear order", they're leaving it up to you whether to use a reflexive or non-reflexive relation symbol. You can do either one, or both, just so long as you don't get confused which is which.