Unit One- Axioms And Postulates Flashcards
(18 cards)
Commutative Property
a+b=b+a; ab=ba
Associative Property
(a+b)+c=a+(b+c); (ab)c=a(bc)
Transitive Property
If a=b and b=c, then a=c
Reflexive Property
a=a
Symmetric Property
If a=b, then b=c
Addition Property of Equality
If a=b and c=d, then a+c=b+d
Subtraction Property of Equality
If a=b and c=d, then a-c=b-d
Multiplication Property of Equality
If a=b and c=d, then ac=bd
Division Property of Equality
If a=b and c (does not equal) zero, then a/c=b/c
Identity Property
a+0=a; and a•1=a
Inverse Property
a+-a=0, and a•1/a=1
Distributive Property
Used to combine like terms
a(b+c)=ab+ac
Existence of Square Roots
For every positive number there exists one and only one positive square root
Trichotomy Property
For every x and y, only one of these can be true;
xy; x=y
Postulate One-The Distance Postulate
To every pair of different points there corresponds a unique positive number
Postulate Two-The Ruler Postulate
The points of a line can be placed in correspondence with the real numbers in such a way that;
1) to every point of a line there corresponds exactly one real number
2) to every real number on a line there corresponds exactly one point
3) the distance between the two points is the absolute value of the difference of the corresponding numbers.
Postulate Three-The Ruler Placement Postualte
Given two points P and Q of a line, the coordinate system can be chosen in such a way that the coordinate of P is zero and the coordinate of Q is positive.
Absolute Value
1) the distance a number is from 0 on the number line
2) |x|=x if x (is greater than or equal to) 0; |x|=-x if x<0
