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 Blacks and Jews in bondage and out of bondage, have been blood histories pursued through our kindred searchings for self-determination. Let this blood be a stain of honor that we share. Let us not now become enemies to ourselves and to each other.”
—June Jordan (b. 1936)
“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)