Fibonacci sequence
You already know what it is!
The famous Fibonacci sequence is a sequence of integers in which each integer is the sum of the two integers before it, starting with \(0\) and \(1.\)
The Fibonacci sequence is defined by the following recurrence
relation for \(n \geq 2\):
$$f_0 = 0$$
$$f_1 = 1$$
$$f_n = f_{n-1} + f_{n-2}$$
⚠ Some define the first Fibonacci numbers to be \(1\) and \(1.\) Fibonacci actually used \(1\) and
\(2.\) On Discretopia, rest assured, we will only ever use \(0\) and \(1\) as the first two
Fibonacci numbers.
As the sequence progresses, the ratio between any two consecutive Fibonacci numbers becomes an ever-better approximation of the golden ratio, \(\varphi.\)
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