function - mapping

the syntax f: D -> R where D and R are sets, it is not required that the entire range be used... D is the set of inputs could be single or pairs or some odd set notation for modulo sets is $$ Z_m $$ where m is the mod

predicate, property, k-ary relations

property or predicate is a true/false relation over some domain. If that domain is k-tuples then it is a k-ary relation that resolves to the same range, true or false

subgraph, simple path, simple cycle, tree def

subset of the nodes, and edges between those nodes of some graph G. Simple path does not repeat nodes. Simple cycle only repeats the start node as the end node, trees are graphs with no simple cycles.

directed graphs, strongly connected, why?

directed paths are same direction, strongly connected DiGraph if a directed path connects every two nodes... useful for depicting binary relations?

Strings

Alphabet is a finit set of symbols, 'string over an alphabet', w^R means reverse, w^k where k is an integer means concatenate k times, prefix defintion should probably be read over a few times...