Irrational number
An irrational number is any real number that cannot be expressed as a fraction of integers.
Real numbers are either rational or irrational, never both. Therefore, if a number is irrational if and only if it is not rational.
Unlike rational numbers, irrational numbers are not defined by an exact expression. This is why proofs involving irrational numbers tend to be indirect, such as proofs by contrapositive.
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