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".

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 …

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 …

Defining a function as a set, and proper use of set notation. Ask Question Asked 12 years, 2 months ago Modified 12 years, 2 months ago

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 $f (a)$.

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 …

Apr 3, 2022 · But function is like something I stated above and set is just a collection of things having something common. How can set do the work of function? I understand that each …

The empty function makes perfect sense with this definition because even though as you say, the empty set is not an ordered pair, that does not matter because still $\emptyset \subseteq …

Oct 29, 2012 · 78 A function on a set involves running the function on every element of the set A, each one producing some result in the set B. So, for the first run, every element of A gets …

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 …