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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