Iterated Function - Definitions in Terms of Iterated Functions

Definitions in Terms of Iterated Functions

Two important functionals can be defined in terms of iterated functions. These are Summation:

\left\{b+1,\sum_{i=a}^b g(i)\right\} \equiv \left( \{i,x\} \rightarrow \{ i+1 ,x+g(i) \}\right)^{b-a+1} \{a,0\}

and the equivalent product:

\left\{b+1,\prod_{i=a}^b g(i)\right\} \equiv \left( \{i,x\} \rightarrow \{ i+1 ,x g(i) \}\right)^{b-a+1} \{a,1\}

Read more about this topic:  Iterated Function

Famous quotes containing the words definitions, terms, iterated and/or functions:

    “What I do not like about our definitions of genius is that there is in them nothing of the day of judgment, nothing of resounding through eternity and nothing of the footsteps of the Almighty.”
    —G.C. (Georg Christoph)

    “Of course I’m a black writer.... I’m not just a black writer, but categories like black writer, woman writer and Latin American writer aren’t marginal anymore. We have to acknowledge that the thing we call “literature” is more pluralistic now, just as society ought to be. The melting pot never worked. We ought to be able to accept on equal terms everybody from the Hassidim to Walter Lippmann, from the Rastafarians to Ralph Bunche.”
    —Toni Morrison (b. 1931)

    “The customary cry,
    ‘Come buy, come buy,’
    With its iterated jingle
    Of sugar-bated words:”
    —Christina Georgina Rossetti (1830–1894)

    “In today’s world parents find themselves at the mercy of a society which imposes pressures and priorities that allow neither time nor place for meaningful activities and relations between children and adults, which downgrade the role of parents and the functions of parenthood, and which prevent the parent from doing things he wants to do as a guide, friend, and companion to his children.”
    —Urie Bronfenbrenner (b. 1917)