[Haskell-cafe] In what language...?
Benedict Eastaugh
ionfish at gmail.com
Tue Oct 26 14:54:50 EDT 2010
On 26 October 2010 19:29, Andrew Coppin <andrewcoppin at btinternet.com> wrote:
>
> I don't even know the difference between a proposition and a predicate.
A proposition is an abstraction from sentences, the idea being that
e.g. "Snow is white", "Schnee ist weiß" and "La neige est blanche" are
all sentences expressing the same proposition.
Propositional logic is quite a simple logic, where the building blocks
are atomic formulae and the usual logical connectives. An example of a
well-formed formula might be "P → Q". It tends to be the first system
taught to undergraduates, while the second is usually the first-order
predicate calculus, which introduces predicates and quantifiers.
Predicates are usually interpreted as properties; we might write
"P(x)" or "Px" to indicate that object x has the property P.
> I also don't know exactly what "discrete mathematics" actually covers.
Discrete mathematics is concerned with mathematical structures which
are discrete, rather than continuous. Real analysis, for example, is
concerned with real numbers—"the continuum"—and thus would not be
covered. Graph theory, on the other hand, concerns objects (nodes and
edges) which have sharp cutoffs—if an edge directly connects two
nodes, there are no intermediate nodes, whereas if you consider an
interval between any two real numbers, no matter how close, there are
more real numbers between them. Computers being the kind of things
they are, discrete mathematics has a certain obvious utility.
Benedict.
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