Binary string
\(0100010001101001011100110110001101110010011001010111010001101111011100000110100101100001\)
A binary string is a string whose alphabet is \(\set{0, 1}.\) Characters in a binary string are called bits. Binary strings of length \(n\) are often called \(n\)-bit binary strings.
The set of all binary strings of length \(k\) is denoted \(B^k.\) Additionally, the set of all binary strings of any length is denoted \(B^*\), defined as the infinite union of all sets \(B^k\) such that \(k \geq 0\): \(B^* = B^0 \cup B^1 \cup B^2 \cup ...\)
Of course, \(B^0 = \set{\lambda}\), because the only string of length \(0\) is the empty string.
⚠ Everything on a computer is stored as binary strings, such as \(1001.\)
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