[Haskell-cafe] In what language...?
andrewcoppin at btinternet.com
Tue Oct 26 15:43:11 EDT 2010
On 26/10/2010 07:54 PM, Benedict Eastaugh wrote:
> 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.
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,
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