notation the following notationsadopted from publications of dijkstraare used in this book in logical expressionsthe character denotes conjunction and is pronounced as and the character oboznachaet otritsanie chitaetsia kak denotes negation and is pronounced as not boldface and are used to denote the universal and existential quantifiers in the following formulasthe left part is the notation used and defined here in terms of the right part note that the left parts avoid the use of the symbol "which appeals to the readers intuition aim < pi pm pm+ pn- the pi are predicatesand the formula asserts that for all indices ranging from given value tobut excluding value pi holds eim < pi pm or pm+ or or pn- the pi are predicatesand the formula asserts that for some indices ranging from given value tobut excluding value pi holds sim < xi xm xm+ xn- min im < xi minimum(xm xn- max im < xi maximum(xm xn-