Examples of Cancellative Monoids and Semigroups
The positive (equally non-negative) integers form a cancellative semigroup under addition. The non-negative integers form a cancellative monoid under addition.
In fact any free semigroup or monoid obeys the cancellative law, and in general any semigroup or monoid embedding into a group (as the above examples clearly do) will obey the cancellative law.
Read more about this topic: Cancellation Property
Famous quotes containing the words examples of and/or examples:
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)
“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (1533–1592)