I encountered the following statement in a non-math book (on digital systems, actually), where the author discusses lattices and Boolean algebras:
The following properties are valid for every finite lattice:
$a+0=a$ and $a.0=0$
I can't see how the proof of these properties could not be valid for an infinite lattice? Could someone give any counter examples to this?
To cut down on the number of unanswered questions on this site, I post this answer.
Consider the lattice $\langle\Bbb Z_-,<\rangle,$ where $\Bbb Z_-$ is the set of negative integers and $<$ is the usual order relation on this set. Readily, there is no such thing as a $0$ of this lattice.