MATH 3RD MID

• Mathematical system


  It has it's own language and properties. it consist of four parts.

  1. Undefined terms
  2. Definitions
  3. Axioms or postulates
  4. Theorems
• Undefined terms


  Is a word which does not require any further explanation or elaborate description.
• Definition


  is a statement that gives clear meaning to a word or a phrase. it has two parts:

  1. The term to be defined
  2. The explanation of the term
• Axioms or Postulates


  Are statement that are accepted without proofs
• Euclid


  He taught in Alexandra in Egypt in his famous work called ELEMENT
• Elements


  Is a complication of knowledge that become the center of mathematical teaching for 2000 years.
• Books I-VI - it deals with plane geometry.
• Books VII-IX - it deals with number theory.
• Books X - It deals with the theory of irrational numbers.
• Books XI-XIII - it deals with three-dimensional geometry
• Axiomatic method - is the proof of a certain result begins from a statement that is known to be true.
• Axioms or postulates - The term ”Posluate“ is usually reserved for geometry and "axion" for all other branches of mathematics.
• The two parts of definition:

  1. The term to be defined
  2. The explanation of the term
• Point - a position in space. It has only location but no dimension, length, width, thickness and does not occupy an area.
• Theorems - Statement can be proven.
• Arrowheads - symbolizes infinity.
• Line segment - two endpoints
• Ray - one endpoint
• Opposite ray - common endpoint
• a+b=b+a/ab=ba

  -Commulative axiom
• (a+b)+c=a+(b+c)

  a(bc)-(ab)c

  -Associative axiom
• a(b+c)=ab+ac

  • Distributive axiom
• a+(-a)=0

  • Inverse
• 5•0=0

  • Zero property
• a+0=a

  a•1=a

  • Identity