Re: [Haskell-cafe] In what language...?

On 26/10/2010 07:54 PM, Benedict Eastaugh wrote:

On 26 October 2010 19:29, Andrew Coppin 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.

Uh, OK.

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.

Already I'm feeling slightly lost. (What does the arrow denote? What's are "the usual logcal connectives"?)

Predicates are usually interpreted as properties; we might write "P(x)" or "Px" to indicate that object x has the property P.

Right. So a proposition is a statement which may or may not be true, while a predicate is some property that an object may or may not possess?

...

I also don't know exactly what "discrete mathematics" actually covers. Discrete mathematics is concerned with mathematical structures which are discrete, rather than continuous.

Right... so its domain is simply *everything* that is discrete? From graph theory to cellular automina to finite fields to difference equations to number theory? That would seem to cover approximately 50% of all of mathematics. (The other 50% being the continuous mathematics, presumably...)