The ruler function on the real line is defined as follows:
Given a rational number in lowest terms, positive, the ruler function outputs the size (length) of a piece resulting from equally subdividing the unit interval into , the number in the denominator, parts. It “ignores” inputs of irrational functions, sending them to 0.
The ruler function is so termed because it resembles a ruler. The following picture might be helpful: if in lowest terms is a reasonably small rational number (which we assume positive). Then it can be “read off” on a ruler whose intervals of one unit size are each equally subdivided into parts measuring units each by
running one’s finger through until the integer preceding it and then
running through to the subsequent th subunit, “left-over” from the division of by .
On the other hand, an irrational number can not be read off from any ruler no matter how fine we subdivide a unit interval in any ruler.
|Date of creation||2013-03-22 18:23:55|
|Last modified on||2013-03-22 18:23:55|
|Last modified by||yesitis (13730)|