On 27/10/2010, at 8:43 AM, Andrew Coppin wrote:
>
> Already I'm feeling slightly lost. (What does the arrow denote? What's are
> "the usual logcal connectives"?)
You mentioned Information Science, so there's a good chance you know something
about Visual Basic, where they are called
AND IMP
OR XOR
NOT EQV
"connective" in this sense means something like "operator".
>
>> 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?
A predicate is simply any function returning truth values.
> is a (binary) predicate. (> 0) is a (unary) predicate.
> 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?
Here's the table of contents of a typical 1st year discrete mathematics book,
selected and edited:
- algorithms on integers
- sets
- functions
- relations
- sequences
- propositional logic
- predicate calculus
- proof
- induction and well-ordering
- recursion
- analysis of algorithms
- graphs
- trees
- spanning trees
- combinatorics
- binomial and multinomial theorem
- groups
- posets and lattices
- Boolean algebras
- finite fields
- natural deduction
- correctness of algorithms
Graph theory is in. Cellular automata could be but usually aren't.
Difference equations are out. Number theory would probably be out
except maybe in a 2nd or 3rd year course leading to cryptography.
> That would seem to cover approximately 50% of all of mathematics. (The other
> 50% being the continuous mathematics, presumably...)
>
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