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Answer by BakerStreet for Intuition behind existence of "function sets"
I am aware that functions are intuitively viewed as processes, but Ifeel like this intuition is not well captured by the definition in settheory, given by a relation (maybe its just me but thats the...
View ArticleAnswer by mls for Intuition behind existence of "function sets"
There are twists and turns in the foundations of mathematics that are only worked out by expansive reading.The "intuitive" picture of functions as "processes" should be contrasted with the historical...
View ArticleAnswer by Kevin for Intuition behind existence of "function sets"
It may help to focus on the axiomatic grounding of these sets. Let's say, for the sake of simplicity, that we already accept the existence of the cartesian product R^2 (that is, the set of all ordered...
View ArticleAnswer by Jo Wehler for Intuition behind existence of "function sets"
It is exactly the idea of a functionF: X ----> Yto formalize the fact that each element y of a second set Y depends on exactly one element x of a first set X: y=F(x).Besides X and Y the function F...
View ArticleIntuition behind existence of "function sets"
The usual axioms ensure the existence of certain sets that serve as functions. For example (which is chosen arbitrarily) the function f which maps real values of x to x^2+2 can be represented by the...
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