Math 2.0

Mathematical logic and foundations Theorem

Associativity of addition

Builds on Addition of natural numbersMathematical induction

Statement

For all natural numbers aa, bb and cc, (a+b)+c=a+(b+c)(a + b) + c = a + (b + c). Here ++ is the addition of natural numbers.

Remarks

The proof from the recursive definition of addition uses induction on cc. Because of this law, we can write a+b+ca + b + c without parentheses. Multiplication of natural numbers is also associative.

Reading path

To understand this page from the ground up, read these 7 pages in order. The foundations come first.

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Definition by recursion, concept, no evidence levelDefinition by recursi…conceptMathematical induction, concept, no evidence levelMathematical inductionconceptNatural numbers, object, no evidence levelNatural numbersobjectPeano axioms, concept, no evidence levelPeano axiomsconceptSuccessor function, definition, no evidence levelSuccessor functiondefinitionAddition of natural numbers, definition, no evidence levelAddition of natural n…definitionAssociativity of addition, statement, no evidence levelAssociativity of addi…statement
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Definition by recursion concept
  2. Mathematical induction concept
  3. Natural numbers object
  4. Peano axioms concept
  5. Successor function definition
  6. Addition of natural numbers definition
  7. Associativity of addition statement

Further reading

  1. Web https://en.wikipedia.org/wiki/Associative_property, Definition
  2. Web https://en.wikipedia.org/wiki/Addition, Associativity
About this page
Tag0C32J27WQC
URIm2://0C32J27WQC
Kindstatement, theorem
WritingW0 stub
MSC03F30
StatusThis copy of the site has no build data. Run m2 status 0C32J27WQC.
UsesAddition of natural numbers, Mathematical induction

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