Books on Amazon
|II 83 f
Function: generality, law. - Any number of x-range is assigned to a number of the y-range - A function is not a variable! (An elliptic function is not an elliptic variable). Function: is unsaturated.
Functional Characters: unsaturated - in connection with numerals: saturated.
Argument: every time a number >value of the function
Caution: It has become common to read the equation "y = f (x)": "y is a function of x". This contains two errors:
1) If the equal sign is translated by the copula.
2) the function with its value is mistaken for an argument. These errors gave rise to the opinion that the function was a number.
Functions of numbers are fundamentally different (because they are unsaturated).
Logic/Grammar: E.g. "Peter plays with Agnes": in the logic both Peter and Agnes can be declared subjects.
Argument/Function: E.g. "(3) to the power of 2": argument expression: "3"
Function expression: "(...) to the power of 2".
E.g. "3 + 2" argument expressions: "2" and "3" - function expression: "+".
E.g. "Peter is asleep" - argument expression: "Peter" - function expression: "is asleep".
E.g. "Everybody loves Agnes" argument expression "loves Agnes" function expression: "everybody"
Function expressions: "+", (..) to the power of"! - verb (sometimes also argument expression)
second order function expression: "everybody", "nobody".
1st order E.g. "is asleep"
2nd order E.g. "everybody", "nobody"._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.
Die Grundlagen der Arithmetik Stuttgart 1987
Funktion, Begriff, Bedeutung Göttingen 1994
Logische Untersuchungen Göttingen 1993