Lesson 2

• set of symbols with attached meanings

  vocabulary
• a set of rules that outline how vocabulary is used

  grammar
• organizes symbols into linear structures

  syntax
• It is able to make a very fine distinction

  precise
• it is able to say things briefly

  concise
• it is able to express complex thoughts with relative ease

  powerful
• It is a property when your answer from calculating non-zero numbers is not zero

  closure properties
• a+b=b+a ; ab=ba

  commutative properties
• a+(b+c)=(a+b)+c

  associative property
• 2+0=2 ; 2(1)=2


  existence of identity elements
• a+(-a)=0 ; a(1/a)=1

  existence of inverse elements
• (3+4)2=(2x3)+(2x4)

  distributive property or DPMA
• a=a


  reflexive property
• a=b ;b=a

  symmetric property
• a=b, then b=c, then a=c

  transitive property
• a+c=b+c ; x-3=y-3 or x+4

  addition property
• a=b; c is not equal to 0, then ac=bc; 2x=2y

  multiplication property
• a finite combination of symbols that is well-formed according to rules that depend on the context

  mathematical expression
• is a fact, name, notation, or usage which is generally agreed upon by mathematicians

  mathematical convention
• It is the hierarchy of mathematical operations. It is the set of rules that determines which operations should be done before or after others.

  order of operations
• 3x+2 (translate)

  two more than thrice a certain number
• x - y=10 (translate)

  the difference of two numbers is 10