Histories
For every, the tuple is called the elementary history of a. It serves as an indicator function for the inclusion of a letter a in an alphabet . That is,
where
Here, denotes the empty string. The history monoid is the free monoid generated by elementary histories. It is clearly a submonoid of the product monoid . The elements of are called global histories, and the projections of a global history are called individual histories.
Read more about this topic: History Monoid
Famous quotes containing the word histories:
“The histories of the lives and fortunes of men are full of instances of this nature,—where favorable times and lucky accidents have done for them, what wisdom or skill could not.”
—Laurence Sterne (1713–1768)
“I read, with a kind of hopeless envy, histories and legends of people of our craft who “do not write for money.” It must be a pleasant experience to be able to cultivate so delicate a class of motives for the privilege of doing one’s best to express one’s thoughts to people who care for them. Personally, I have yet to breathe the ether of such a transcendent sphere. I am proud to say that I have always been a working woman, and always had to be ...”
—Elizabeth Stuart Phelps (1844–1911)
“As soon as histories are properly told there is no more need of romances.”
—Walt Whitman (1819–1892)