From Semigroup To Group, Through Power Notation

If we consider the exponential notation used in abstract algebra, we get a nice mnemonic for semigroups, monoids, and groups:

  • Semigroup: Only positive powers are defined
  • Monoid: The identity element makes defined, so non-negative powers are defined
  • Group: inverses define negative powers, so all integer powers are defined

By remembering the completion of the natural numbers into the integers, we can remember what exactly defines semigroups, monoids, and groups (I know I mix them up all the time).

Related Posts

How to change tabs to spaces

Another Way to Write Conditional Probability

Notes for May 9, 2019

A tool to look at random images


e-ink reminisces

Edwin Edwards

Middle School by Bo Burnham

How to Disable Disqus Ads on your Blog

Derivation of Reservoir Sampling