x greater than 0 implies x greater than or equal to 0

Question

Why is this statement true? All we know is that x is greater than 0, and it does seem like the converse muse be true.

Answer 1

No matter what statements $p,q$ are, one can say if $p$ then ($p$ or $q$). Apply this to $x>0$ for $p$ and $x=0$ for $q.$

Answer 2

For the binary relation $''\geq''$ we have $$ ''\geq'' = ''>'' \cup \, ''='' $$ Thus $''>''\, \subseteq \, ''\geq''$.