2 citations · 3 across the 8 of their papers we have counts for
8 papers
The Infinite in Sciences and Arts
W. Mueckenheim
Actual infinity in its various forms is discussed, searched and not found.
Physical Constraints of Numbers
W. Mueckenheim
All sciences need and many arts apply mathematics whereas mathematics seems to be independent of all of them, but only based upon logic. This conservative concept, however, needs t…
On Cantor's Theorem
W. Mueckenheim
The famous contradiction of a bijection between a set and its power set is a consequence of the impredicative definition involved. This is shown by the fact that a simple mapping b…
A severe inconsistency of transfinite set theory
W. Mueckenheim
Transfinite set theory including the axiom of choice supplies the following basic theorems: (1) Mappings between infinite sets can always be completed, such that at least one of th…
The Meaning of Infinity
W. Mueckenheim
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 infinit…
On Cantor's important proofs
W. Mueckenheim
It is shown that the pillars of transfinite set theory, namely the uncountability proofs, do not hold. (1) Cantor's first proof of the uncountability of the set of all real numbers…