Artículos con la etiqueta ‘matemática no-standart’

Alternative Mathematics without Actual Infinity

Por • 13 abr, 2012 • Category: Opinion

An alternative mathematics based on qualitative plurality of finiteness is developed to make non-standard mathematics independent of infinite set theory. The vague concept «accessibility» is used coherently within finite set theory whose separation axiom is restricted to definite objective conditions. The weak equivalence relations are defined as binary relations with sorites phenomena. Continua are collection with weak equivalence relations called indistinguishability. The points of continua are the proper classes of mutually indistinguishable elements and have identities with sorites paradox. Four continua formed by huge binary words are examined as a new type of continua. Ascoli-Arzela type theorem is given as an example indicating the feasibility of treating function spaces.