Definition:Bottom of Lattice
(Redirected from Definition:Null of Lattice)
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Definition
Let $\struct {S, \vee, \wedge, \preceq}$ be a lattice.
Definition 1
Let $S$ admit a smallest element $\bot$.
Then $\bot$ is called the bottom of $S$.
Definition 2
Let $\vee$ have an identity element $\bot$.
Then $\bot$ is called the bottom of $S$.
Also known as
The bottom of a lattice is also known as a null.
Some sources denote this bottom or null by $0$.
Also see
- Results about the bottom of a lattice can be found here.
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