Tag: Real number

Goedel’s Incompeteness theorem surpassed?
Gödel’s Incompleteness Theorems are one of the cornerstone’s of modern mathematical thought but it is also a major blot on the mathematical landscape – as it establishes an inherent limit on the ability of mathematicians to describe the mathematical world: the first theorem (often thought of as the theorem) states that no consistent (ie selfcontained)…

The diagonal proof
I am just reading Computability and Logic and it (or at least the old, 1980, edition I am reading) has a rather laboured explanation of Cantor’s 1891 proof of the nonenumerability of real numbers (the diagonal proof) so to reassure myself and because it is interesting I thought I’d set out a version here (closely…

The importance of Turing’s findings
Yesterday I was speaking to a friend – who knows about computers but not about computer science – who told me this blog was just too difficult: so I thought I’d seek to order my own thoughts after reading The Annotated Turing and assist humanity in general (!) by writing a piece that explains what…