Floor function
The floor function is a function \(floor: \mathbb R \rightarrow \mathbb Z\) that rounds down a real number to the nearest integer. To be specific, \(floor(x)\), abbreviated as \(\lfloor {x}\rfloor \), returns the largest integer \(y\) such that \(y \leq x.\) The floor function's counterpart is the ceiling function.
For example, \(\lfloor {7.83}\rfloor = 7\), \(\lfloor {5}\rfloor = 5\), \(\lfloor {-2.2}\rfloor = -3\) and \(\lfloor {-9}\rfloor = -9.\)
⚠ When the floor function is given an integer as its input, it returns the exact same integer as its
output.
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