Relative price action forward or backward from a time forms a continuous function f, with f(0) = 0.
Key to trade management by stops and targets are the extremes of this price action. Let E be the set of positive reals e s.t. f(e) does not lie in f( [0, e) ). An extreme of a continuous function f: [0, Inf) -> (-Inf, Inf) is an extreme e s.t. all extremes in some future neighbourhood of e are of the opposite sign.
The image under f of E consists of semi-open intervals of the forms (p_i, p_i+1] and [n_i+1, n_i), where {p_I} are positive extremes and {n_i} are negative extremes and the latter interval is in reverse temporal order (taking time as the domain of f).
