mu-Operator
المؤلف:
Mendelson, E
المصدر:
Introduction to Mathematical Logic, 4th ed. London: Chapman & Hall, 1997.
الجزء والصفحة:
...
12-2-2022
947
mu-Operator
Let 
be a function such that for any 
, ..., 
, there is at least one 
such that 
. Then the 
-operator 
gives the least number 
such that 
. More generally, for a relation 
, the 
-operator gives the least 
, if any, such that 
is true, and this least value of 
is denoted 
(Mendelson 1997, p. 175).
For example, given a criterion crit and a list ![<span style=]()
{" src="https://mathworld.wolfram.com/images/equations/Mu-Operator/Inline16.svg" style="height:22px; width:6px" />x1, x2, ..., xn![<span style=]()
}" src="https://mathworld.wolfram.com/images/equations/Mu-Operator/Inline17.svg" style="height:22px; width:6px" />, the 
-operator could be written in the Wolfram Language as Select[Sort[![<span style=]()
{" src="https://mathworld.wolfram.com/images/equations/Mu-Operator/Inline19.svg" style="height:22px; width:6px" />x1, x2, ..., xn![<span style=]()
}" src="https://mathworld.wolfram.com/images/equations/Mu-Operator/Inline20.svg" style="height:22px; width:6px" />], crit, 1].
REFERENCES
Mendelson, E. Introduction to Mathematical Logic, 4th ed. London: Chapman & Hall, 1997.
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