Ceiling function
The ceiling function is a function \(ceiling: \mathbb R \rightarrow \mathbb Z\) that rounds up a real number to the nearest integer. To be specific, \(ceiling(x)\), abbreviated as \(\lceil {x}\rceil \), returns the smallest integer \(y\) such that \(y \geq x.\) The ceiling function's counterpart is the floor function.
For example, \(\lceil {7.83}\rceil = 8\), \(\lceil {5}\rceil = 5\), \(\lceil {-2.2}\rceil = -2\) and \(\lceil {-9}\rceil = -9.\)
⚠ When the ceiling 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
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Number Theory
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Combinatorics
Graph Theory
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Complete graph •
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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