Some Elementary Informal Set Theory

Set theory is due to Georg Cantor. “Elementary” in the title above does not apply to the body of his work, since he went into considerable technical depth and mathematical sophistication in this, his new theory. It applies however to our coverage in this volume as we are going to restrict ourselves to elementary topics only. Cantor’s Set Theory contains quite a few contradictions widely referred to in the literature as paradoxesParadox or antinomiesAntinomy, some of considerable consequence. The next section is about the least technical, hence the most elementary of all to describe, and most fundamental of these antinomies contained in Cantorian set theory and was discovered by Bertrand Russell.