Is the closed half real line a meet-semilattice?

81 Views Asked by At

Extremely simple question

Is $\mathbb{R}_{\geq 0} = [0, \infty)$ a meet-semilattice?

Consider any two numbers $x,y \in \mathbb{R}_{\geq 0}$, $x \land y = \inf\{x,y\} = x$ if $x \leq y$ and $y$ if $y < x$

Just to make sure before I use a new concept, because nothing is written about this.

1

There are 1 best solutions below

5
On BEST ANSWER

Yes, it is: the meet of two non-negative real numbers is simply the minimum of the two numbers. $\Bbb R$ is also a meet semilattice. Indeed, any linear order is a lattice: the meet of two elements is their minimum, and the join is their maximum.