Math often feels difficult to me because I try to put all of my understandings into plain English sentences, and mathematical understanding is sometimes unintuitive.

For example, consider the function $f$.

Define $f$ as

{$ A,B,C,…,Z $} $\to$ {$ 0,1,2,…,25 $}

(The set A consisting of all elements of the English alphabet maps to the set B consisting of the integers 0 through 25, inclusive.)


$A\mapsto 0 $, $B\mapsto 1 $, $C\mapsto 2 $, …, $Z\mapsto 25 $

After only a few moments, this definition is easy to grasp. But, it’s not so easy to translate what we know about $f$ into English sentences. Go ahead, I challenge you!

Did you try it? Let me know if you did. Here’s my own account:

Map from the English alphabet to the set S={0,…,25}

$\forall x$ $\in S$, sort the elements of the set S and locate and return of element x by it’s relative fixed position in the newly ordered set $S’$