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:

    “The loosening, for some people, of rigid role definitions for men and women has shown that dads can be great at calming babies—if they take the time and make the effort to learn how. It’s that time and effort that not only teaches the dad how to calm the babies, but also turns him into a parent, just as the time and effort the mother puts into the babies turns her into a parent.”
    —Pamela Patrick Novotny (20th century)

    “If you want to be on good terms with everyone in this world, sell goods on credit and never ask for payment.”
    —Chinese proverb.

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

    “One of the most highly valued functions of used parents these days is to be the villains of their children’s lives, the people the child blames for any shortcomings or disappointments. But if your identity comes from your parents’ failings, then you remain forever a member of the child generation, stuck and unable to move on to an adulthood in which you identify yourself in terms of what you do, not what has been done to you.”
    —Frank Pittman (20th century)