Element
An element, or member, of a set (or in general, any collection of objects) is a distinct object that belongs to it. If \(a\) is an element of the set \(A\), this relation is written as \(a \in A.\) Usually, elements are symbolized by lowercase letters.
As a consequence of the definition of the empty set, for any element \(a\), \(a \notin \emptyset.\)
⚠ Since elements can be anything, they can also be sets! That's right – it's possible for a set to
contain sets as elements. However, the elements of a set which is itself an element of some larger set
are not to be considered elements of that larger set. Keep that in mind.
Logic & Proofs
Integer •
Rational number •
Inequality •
Real number •
Theorem •
Proof •
Statement •
Proof by exhaustion •
Universal generalization •
Counterexample •
Existence proof •
Existential instantiation •
Axiom •
Logic •
Truth •
Proposition •
Compound proposition •
Logical operation •
Logical equivalence •
Tautology •
Contradiction •
Logic law •
Predicate •
Domain •
Quantifier •
Argument •
Rule of inference •
Logical proof •
Direct proof •
Proof by contrapositive •
Irrational number •
Proof by contradiction •
Proof by cases •
Summation •
Disjunctive normal form
Set Theory
Set •
Element •
Empty set •
Universal set •
Subset •
Power set •
Cartesian product •
String •
Binary string •
Empty string •
Set operation •
Set identity •
Set proof
Functions
Algorithms
Relations
Number Theory
Induction
Combinatorics
Graph Theory
Graph •
Walk •
Subgraph •
Regular graph •
Complete graph •
Empty graph •
Cycle graph •
Hypercube graph •
Bipartite graph •
Component •
Eulerian circuit •
Eulerian trail •
Hamiltonian cycle •
Hamiltonian path •
Tree •
Huffman tree •
Substring •
Forest •
Path graph •
Star •
Spanning tree •
Weighted graph •
Minimum spanning tree •
Greedy algorithm •
Prim's algorithm
Recursion