Study your flashcards anywhere!

Download the official Cram app for free >

  • Shuffle
    Toggle On
    Toggle Off
  • Alphabetize
    Toggle On
    Toggle Off
  • Front First
    Toggle On
    Toggle Off
  • Both Sides
    Toggle On
    Toggle Off
  • Read
    Toggle On
    Toggle Off
Reading...
Front

How to study your flashcards.

Right/Left arrow keys: Navigate between flashcards.right arrow keyleft arrow key

Up/Down arrow keys: Flip the card between the front and back.down keyup key

H key: Show hint (3rd side).h key

A key: Read text to speech.a key

image

Play button

image

Play button

image

Progress

1/22

Click to flip

22 Cards in this Set

  • Front
  • Back
Closure Axiom of Addition
CLAA

If a+b=c, then c is a real number
Closure Axiom of Multiplication
ClAM

If ab=c, then c is a real number
Commutative Axiom of Addition
CAA

a+b=b+a
Commutative Axiom of Multiplication
CAM

ab=ba
Associative Axiom of Addition
AAA

(a+b)+c=a+(b+c)
Associative Axiom of Multiplication
AAM

(ab)c=a(bc)
Axiom of Zero for Addition
(Identity for Addition)
A0A
(Id+)

a+0=0+a=a
Axiom of One for Multiplication
(Identity for Multiplication)
A1M
(Idx)

ax1=1a=a
Axiom of Additive Inverses
AAI

a+(-a)=-a+a=0
Axiom of Multiplicative Inverses
AMI

*A cannot equal 0*

a x 1/a = 1/a x a =1
Distributive Axiom of Multiplication over Addition
DAMA

a(b+c)=ab+ac
Reflexive Axiom
a=a
Symmetric Axiom
If a=b, then b=a
Transitive Axiom
If a=b and b=c, then a=c
Definition of Subtraction
a-b=a+(-b)
Definition of Division
a(division symbol)b or a/b = a x 1/b
Binary Operation
A rule for combining two real numbers (or things) to get a unique (one and only one!) real number (or thing)
upside down A
means "for all, for each, for every, for any..."
universal quantifier
backwards E
means "there exists for at least one, for some..."
backwards E with !
means "there is exactly one x, or a unique x"
straight vertical line
means "such that"
Ring
system in math with these axioms is called a ring