ABSTRACT
Iterative methods are often used to prove the existence of a solution to linear/nonlinear system of equations, ordinary/partial differential equations and many others. The iterations are usually indexed by integers and the basic tool is the contraction mapping theorem. A continuous version (without the indexing by integers) was proposed by the famous Czech mathematician Vlastimil Pták in 1974 during his quantitative study of the closed graph theorem in functional analysis (Pták, 1974). For a biography on Pták see (Vavrˇín, 1996). In the following we shall trace a path that will lead to this principle of nondiscrete induction.
