Impossibilities, mathematics, and logic
preprint
OA: closed
CC-BY-4.0
Abstract
Mathematics is known for its rigor. Owing to its rigor, mathematics is both loved and feared. Proof holds a pivotal position in the whole of mathematical rigor. Proof is required for something to be possible. Interestingly, proof is equally important and required for something to be declared impossible. In this paper, certain beautiful examples of impossibilities are mentioned, which include, among others, the impossibility of the denumerability of real numbers, squaring a circle, and doubling a cube.
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Source provenance
- europepmc
- last seen: 2026-05-19T01:45:01.086888+00:00
- unpaywall
- last seen: 2026-05-22T02:00:06.705733+00:00
License: CC-BY-4.0