Arithmetic Glossary
Natural numbers
The numbers generated from a base element (0) by repeated application of a successor operation.
Successor
An operation that produces the next natural number after .
Peano axioms
A set of axioms that define the natural numbers via 0, successor, and induction.
Induction
A proof principle that allows reasoning about all natural numbers by proving a base case and a step case.
Recursion
A method of defining functions on natural numbers by specifying a base value and a rule for the successor.
Semiring
An algebraic structure with addition and multiplication, like the natural numbers, where addition is commutative and multiplication distributes over addition.
Zero
The base natural number, written 0.
Addition
An operation that combines two numbers into a sum.
Multiplication
Repeated addition as a single operation.