We find the smallest field containing the number 1 when using the usual addition and multiplication of real numbers.

# Blog

## Integral Domain of Integers

We show that the integers modulo any prime forms an integral domain under addition and multiplication modulo p.

## A Ring of Matrices

We show, step-by-step, that the set of all 2 x 2 matrices with real entries forms a ring under addition and multiplication.

## Representations of Cyclic Groups

We show that every cyclic group is isomorphic to either the set of integers or the set of integers mod some integer under addition.

## Setting off for the New World

I take some time away from doing algebra to look at an upcoming video game, New World, and discuss its potential.