Mathematics Made Difficult is a book by Carl E. Linderholm that uses advanced mathematical methods to prove results normally shown using elementary proofs.

Although the aim is largely satirical,[1][2] it also shows the non-trivial mathematics behind operations normally considered obvious, such as numbering, counting, and factoring integers.

Linderholm discusses these seemingly-obvious ideas using concepts like categories and monoids.

Thus the remainder left by any number on division by 2 is either 0 or 1.

Hence the quotient ring Z/2Z, where 2Z is the ideal in Z generated by 2, has only the elements [0] and [1], where these are the images of 0 and 1 under the canonical quotient map.