The Meaning of Infinity

Details The Meaning of Infinity The Meaning of Infinity

2004-03-15

arxiv.org/abs/math/0403238v2

Mathematics

General Mathematics

Scientific paper

The notions of potential infinity (understood as expressing a direction) and actual infinity (expressing a quantity) are investigated. It is shown that the notion of actual infinity is inconsistent, because the set of all (finite) natural numbers which it is ascribed to, cannot contain an actually infinite number of elements. Further the basic inequality of transfinite set theory aleph0 < 2^aleph0 is found invalid, and, consequently, the set of real numbers is proven denumerable by enumerating it.

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