Definition:Atom of Lattice/Also defined as

Atom of Lattice: Also defined as

Some sources omit the stipulation that an atom of a lattice is not the bottom of that lattice.

By definition of bottom, there exist no $B$ such that $B \prec \bot$.

Hence $B = \bot$ is vacuously true.

Hence:

$\forall B \in S: B \prec \bot \implies B = \bot$

is true.

That is, without explicitly stating that an atom is not the bottom, $\bot$ would be classified as an atom vacuously.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): atom
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): atom