Raising

That is to say E a together ordered and F part of E , a raising ( resp. undervaluing ) F is an element X of E such as all the elements of F are lower ( resp. higher) than X .

Either $\backslash \; (E,\; \backslash \; Leq)$ an ordered unit and $F\; \backslash \; subseteq\; E$, $\backslash \; X\; \backslash \; in\; E$ is:

• one undervaluing of $\backslash \; F$ if $\backslash \; forall\; there\; \backslash \; in\; F,\; X\; \backslash \; Leq\; there$;
• one raising of $\backslash \; F$ if $\backslash \; forall\; there\; \backslash \; in\; F,\; there\; \backslash \; Leq\; X$.

Vocabulary

• If   F has one raising X   then it is said that   F is a raised left
• If   F has one undervaluing X   then it is said that   F is an undervalued left

Examples

• for the interval ] 0; 10 part of the whole of [[the Real number|real numbers] ordered by the usual order ≤: 10 and 11 are raising whereas 0 and -7 are undervaluing ,
• $does\; not\; have\; raising\; in$ \backslash \; mathbb\; \{R\}$.$

Related concepts

• upper Limit
• maximum element
• larger element

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