Index

A

addition - binary algebra, [1], [2] Algorithm Design Algorithms & Data Structures, [1] and (logical operator), [1]

AND gate antecedent antisymmetric relation argument associative operator

B

base case, [1], [2] base-2 number biconditional operator, [1], [2] bijective bijective function binary number, [1] binary relation binary search tree binary tree

bit bitwise logical operator Boole - George, [1], [2] Boolean algebra, [1], [2] and logic circuits in predicate logic in set theory bound variable brace symbol, [1]

C

calling a subroutine Cantor - George, [1], [2] cardinality, [1], [2] Cartesian product children Church - Alonzo CNF combinatorial logic circuit combinatorics complement composition compound proposition computability computable languages Computer Organisation, [1], [2] conclusion, [1], [2]

conditional conditional operator conjunction conjunctive normal form consequent contingency contradiction contrapositive converse coordinates Coq corollary countable set countably infinite counterexample, [1] cross product Cruyff - Johan

D

DAG database, [1], [2] Database Management System DBMS deduction, [1], [2] Delft DeMorgan's Laws, [1], [2] diagonalization direct proofs Directed Acyclic Graph disjoint sets

disjunction disjunctive normal form distributive law, [1], [2], [3] divisible by m DNF domain, [1] domain of discourse dominos analogy for mathematical induction double negation duality

E

edge edges element (of a set) empty set entity variable equals sign equivalence class equivalence relation, [1]

Euclid, [1] even evenly divides excluded middle - law of exclusive or operator existence proof existential quantifier Explosion - Principle of extensional definition

F

false (logical value) feedback in circuits Feijenoord Feyenoord, [1], [2], [3] Fibonacci sequence finite set first-class citizen first-class object, [1] font formal proof

formal structure free variable Frege - Gottlob, [1], [2] function, [1], [2] in computer programming on graphs on trees partial functional programming functionally complete, [1] funtionally complete

G

Galileo Gauss - Carl Godel - Kurt, [1]

graph, [1], [2], [3] directed acyclic undirected

H

halting problem

hexadecimal number hypothesis, [1]

I

identity law if and only if iff, [1] image implication incompleteness theorems indirect proof induction second form induction - structural induction hypothesis

inductive case inductive hypothesis infinite set injective integers intensional definition intersection, [1] invalid argument invariant, [1] inverse irrational numbers iteration

J

Java, [1], [2], [3], [4], [5], [6]

JavaScript

K

Karnaugh-map

Khan Academy

L

laws of Boolean Algebra leaf leaf node left subtree lemma linked data structures, [1] logic circuit and compound propositions for an input/output table simplifying logic gate, [1]

logical connective logical deduction logical equivalence, [1], [2], [3], [4] and logical deduction in predicate logic, [1] logical operator bitwise logically implies loop invariant Lucas - 'Edouard Luyben - Karel

M

main connective mapping mathematical generality mathematical induction

mathematical structure member (of a set) modus ponens, [1] modus tollens, [1]

N

n-ary relation NAND gate natural language natural numbers necessary necessity negation of quantified statements neighbour

node, [1] internal leaf, [1] non-Euclidean geometry none, [1], [2] NOR gate not (logical operator) NOT gate null pointer

O

obviousness, [1] octal number odd one-place predicate one-to-one one-to-one correspondence onto function

open statement or (logical operator), [1] inclusive vs. exclusive OR gate ordered n-tuple ordered pair ordered triple

P

parameter parentheses, [1], [2], [3], [4] partial function partial order partition path, [1] Peirce - Charles, [1] pigeonhole principle power set precedence rule, [1], [2] predicate, [1], [2], [3], [4] predicate calculus predicate logic premise, [1], [2] primary key prime Principle of Explosion, [1] principle of mathematical induction see mathematical induction

product (of sets) Prolog, [1] Prometheus proof, [1], [2], [3] by contradiction by contrapositive by division into cases by generalisation examples proof assistants proper subset proposition, [1] equivalent to one in DNF for a logic circuit propositional logic, [1], [2], [3] propositional variable prototype Python

Q

quantifier in English on a two-place predicate

quantifiers, [1] query - database query language

R

range rational numbers real numbers recursion recursive definition recursive definition recursive subroutine reflexive relation

relation, [1] relational database right subtree root, [1] round brackets Rubik's Cube Russell - Bertrand, [1], [2], [3] Russell's Paradox, [1]

S

search tree set of functions from A to B set difference set theory set-builder notation sets simple term Sinterklaas, [1] situation Socrates SQL strong induction

structural induction Structured Query Language subroutine subset substitution law, [1] subtree sufficiency sufficient summation notation surjective syllogism symmetric difference symmetric relation

T

Tarski - Alfred, [1] Tarski's world tautology, [1], [2], [3] ternary relation topological ordering, [1] total function total order Towers of Hanoi transitive closure transitive relation

tree, [1], [2], [3] trees true (logical value) truth table, [1], [2] and logic circuits of a tautology TU Delft tuple, [1] tuples Turing - Alan, [1] Turing machine

U

uncountable set unicorn, [1], [2], [3]

union, [1] universal quantifier universal set

V

valid argument, [1] value (of a function) variable, [1] propositional

Venn diagram, [1] vertex vertices von Neumann - John

W

wires in computers

Z

Zadeh - Lotfi