ABSTRACT:
Since the beginning of the twentieth century several positions w.r.t. the foundations of mathematic have been formulated which might be said to be versions of constructivism. Typically a constructivist view demands of mathematics some form of explicitness of the objects studied, they must be concretely representable, or explicitly definable, or capable of being viewed as mental constructions. In this master thesis, in chapter 1, we attempt to illustrate the idea of constructivity by means of some quite elementary examples and next we briefly introduce the three most important varieties of constructivism: First, Intuitionism (INT), due to the Dutch mathematician L.E.J. Brouwer, insisting that mathematics is a mental construction throughout; a consequent development of this point of view leads to a mathematical practice which deviates from and ?(1)=1, and e the set of all ?’s i for which there exists x in [0,1] such that ?(x)=1/2. It is well-known that there are functions i which cannot been proved to be belonged to , and that with the help of Brouwr’s continuity principles . Based on [20], it is shown that in the presence of Brouwer’s continuity principle it can be defined uncountabaly many subsets of with the property . For this purpose, some special ), i.e. .
