In constructive mathematics even very small sets can be quite a bit more interesting than in classical mathematics. Since you will not believe me that sets with at most one element are very interesting, let us look at the set of truth values, which has “two” elements.
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What constructive mathematics actually says about the law of excluded [...] I have found a good way to write math in web pages. ASCIIMathML is a piece of javascript that translates simple-minded Latex-like ASCII math to MathML, but only if the browser supports MathML. Since the input syntax is very simple, the expressions are quite readable in the raw form, as well. For example, if I [...] Abstract: Computability theory, which investigates computable functions and computable sets, lies at the foundation of computer science. Its classical presentations usually involve a fair amount of Gödel encodings which sometime obscure ingenious arguments. Consequently, there have been a number of presentations of computability theory that aimed to present the subject in an abstract and conceptually [...] |
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