Category:Definitions/Infima

From ProofWiki
Jump to navigation Jump to search

This category contains definitions related to Infima.
Related results can be found in Category:Infima.


Let $\struct {S, \preceq}$ be an ordered set.

Let $T \subseteq S$.


An element $c \in S$ is the infimum of $T$ in $S$ if and only if:

$(1): \quad c$ is a lower bound of $T$ in $S$
$(2): \quad d \preceq c$ for all lower bounds $d$ of $T$ in $S$.


If there exists an infimum of $T$ (in $S$), we say that $T$ admits an infimum (in $S$).