Dirichlet Function
Let 
and 
be Real Numbers (usually taken as 
and 
). The Dirichlet function is defined by
The function is Continuous at Irrational
and discontinuous atRational points. The function can be written analytically as
Because the Dirichlet function cannot be plotted without producing a solid blend of lines, a modified version can be defined as
(Dixon 1991), illustrated above.See also Continuous Function, Irrational Number, Rational Number
References
Dixon, R. Mathographics. New York: Dover, pp. 177 and 184-186, 1991. Tall, D. ``The Gradient of a Graph.'' Math. Teaching 111, 48-52, 1985.
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