# 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 $\ \left(E, \ Leq\right)$ an ordered unit and $F \ subseteq E$, $\ X \ in E$ is:

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

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 ,
• $does not have raising in\ mathbb \left\{R\right\}.$

## Related concepts

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