Summation - Formal Definition

Formal Definition

If the iterated function notation is defined e.g. and is considered a more primitive notation then summation can be defined in terms of iterated functions as:

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

Where the curly braces define a 2-tuple and the right arrow is a function definition taking a 2-tuple to 2-tuple. The function is applied b-a+1 times on the tuple {a,0}.

Famous quotes containing the words formal and/or definition:

“Two clergymen disputing whether ordination would be valid without the imposition of both hands, the more formal one said, “Do you think the Holy Dove could fly down with only one wing?””
—Horace Walpole (1717–1797)

“Scientific method is the way to truth, but it affords, even in
principle, no unique definition of truth. Any so-called pragmatic
definition of truth is doomed to failure equally.”
—Willard Van Orman Quine (b. 1908)