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mu-Operator


Let g(x_1,...,x_n,y) be a function such that for any x_1, ..., x_n, there is at least one y such that g(x_1,...,x_n,y)=0. Then the mu-operator muy(g(x_1,...,x_n,y)=0) gives the least number y such that g(x_1,...,x_n,y)=0. More generally, for a relation R, the mu-operator gives the least y, if any, such that R(x_1,...,x_n,y) is true, and this least value of y is denoted muyR(x_1,...,x_n,y) (Mendelson 1997, p. 175).

For example, given a criterion crit and a list {x1, x2, ..., xn}, the mu-operator could be written in the Wolfram Language as Select[Sort[{x1, x2, ..., xn}], crit, 1].


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References

Mendelson, E. Introduction to Mathematical Logic, 4th ed. London: Chapman & Hall, 1997.

Referenced on Wolfram|Alpha

mu-Operator

Cite this as:

Weisstein, Eric W. "mu-Operator." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Mu-Operator.html

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