Third edition of Artificial Intelligence: foundations of computational agents, Cambridge University Press, 2023 is now available (including the full text).
16.1 Discrete Mathematics
The mathematical concepts we build on include:
- sets
- A set has elements (members). We write s ∈S if s is an element of set S. The elements in a set define the set, so that two sets are equal if they have the same elements.
- tuples
- An n-tuple is an ordered grouping of n elements, written ⟨x1,...,xn⟩. A 2-tuple is a pair, and a 3-tuple is a triple. Two n-tuples are equal if they have the same members in the corresponding positions. If S is a set, Sn is the set of n-tuples ⟨x1,...,xn⟩ where xi is a member of S. S1 ×S2×...×Sn is the set of n-tuples ⟨x1,...,xn⟩ where each xi is in Si.
- relations
- A relation is a set of n-tuples. The tuples in the relation are said to be true of the relation.
- functions
- A function, or mapping, f from set D, the domain of f, into set R, the range of f, written f:D →R, is a subset of D×R such that for every d∈D there is a unique r∈R such that ⟨d,r⟩ ∈f. We write f(d)=r if ⟨d,r⟩∈f.
While these may seem like obscure definitions for common-sense concepts, you can now use the common-sense concepts comfortable in the knowledge that if you are unsure about something, you can check the definitions.
