ProofWiki - Relations
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Category index on ProofWiki collecting formal definitions and fully written proofs about relations: reflexivity, symmetry, transitivity, equivalence relations, orderings, composition and inverses. Useful for checking a precise statement or seeing how a standard result is proved step by step.
More resources on Relations
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
PlanetMath - Binary Relation
Encyclopedia entry on binary relations in set theory
Mathematics for Computer Science (MIT 6.042J)
Discrete mathematics for computer science with an emphasis on definitions and proofs: logic, induction, sets and relations, graph theory, modular arithmetic, asymptotics, counting and discrete probability. 25 lecture videos, problem sets and exams with solutions build fluency in writing proofs.
Elements of Set Theory
Undergraduate textbook developing axiomatic Zermelo-Fraenkel set theory from the ground up. Covers relations and functions, the construction of the natural and real numbers, cardinals, ordinals and the axiom of choice, leaving the reader able to work with sets rigorously.
Introduction to Mathematical Thinking
Stanford course by Keith Devlin on how mathematicians reason, starting with the logic of language (and, or, not, implication, quantifiers) and moving to the structure of proofs, including contradiction and induction. Learners become able to read, construct and critique simple mathematical proofs.