A function that assigns the number 1 to a set if it contains the word "zebra", and assigns the number 0 otherwise. We could call this the "characteristic function" for the word "zebra".

A function $f:A\rightarrow B$ 'sends' each element of $A$ to an element $f (a)$ of $B$. If $a\in A$ and set $B$ is finite with cardinality $|B|$ then there are $|B|$ choices for $f (a)$.

Defining a function as a set, and proper use of set notation. Ask Question Asked 12 years, 3 months ago Modified 12 years, 3 months ago

May 7, 2015 · So this is a function from the set of natural number to its power set, primes(5) = 2,3,5 p r i m e s (5) = 2, 3, 5. Another example: take A A to be the set of professional football players, and …

Basically, my confusion is this: I thought that a function was specified by a finite string. Thus, the reason that we need the Axiom of Choice to select a set from an infinite number of socks is that there's no …

Jan 21, 2024 · The rule is the syntax and the set is the semantics. But in modern mathematical parlance, the word "function" refers to the semantics and not the syntax. This is because the set of functions …

Sep 1, 2013 · @Stefan: But what good is one function? Is all you ever use in mathematics is one function? Why was set theory developed as a foundation for mathematics anyway? So we can talk …

Apr 30, 2017 · I am reading an introduction to measure theory, which starts by defining $\\sigma$-rings then additive set functions and their properties which are given without proof. I was able to prove two …

Jul 21, 2022 · For a decent description of what a function really is, consider looking at Halmos's Naive Set Theory. When I say "what it really is", I mean "a set theoretic object that has all the properties …

Jul 26, 2018 · From the quote, it does appear that the author is subscribing more to the point of view of type theory that functions should be considered a primitive notion, and graphs of functions should be …