Effectively calculable
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In mathematics, a function is said to be effectively calculable if there is an effective method or procedure, i.e. an algorithm, for calculating the function. For example, arithmetical division is effectively calculable since for any two numbers m, n, there is an effective procedure, e.g. long division, for calculating the value of m/n.
The intuitive notion of effective calculability should not be confused with the mathematical notion of effective computability in any of its equivalent senses (e.g. in the sense of Turing computability). The thesis that these notions are equivalent, or that the mathematical notion completely captures the intuitive one in extension, is known as the Church-Turing thesis. It is equivalent to Markov's thesis, viz., that any effective procedure can be specified by a Markov algorithm.
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