Lecture 1: Real Numbers and its subsets Flashcards
1
Q
what is a real number system
A
- collection of all possible numbers
- can be represented by points on a line = a real number line
2
Q
strict inequalities
A
- a<b a is less than b
- a>b a is greater than b
- double inequalities a<x<b
3
Q
non strict inequalitites
A
- x <- r = equal to or less than 5
can be a non strict double inequality as well
4
Q
intervals
A
{ I } is read as such that
- by a short notion with open brackets
inside { } = [ ]
- outside the brackets { } = ( )
5
Q
what are the three ways to write intervals
A
- as a set using curly brackets { } and a I
- by using short notation with open brackets ( ) , closed [ ] and their combinations
- by graphing it on a real line
6
Q
intervals on number lines
A
- { } or [ ] open circle
- [ ) solid circle
7
Q
ordered pairs
A
- ( a b ) of two real numbers is defined by the property (a b) =/ (b a)
- the collection of all ordered pairs (x y) is donated by R2 and is known as the cartesian product of R
- geometrically or graphically we describe R2 with two real lines intersecting each other perpendicularly
8
Q
slope
A
given two ordered pairs (x1, y1) and (x2, y2)
y2-y1/x2-x1
9
Q
horizontal lines
A
y=b
10
Q
vertical lines
A
x=a
