Section 1.1: Set builder and Interval Notation
NO! (∞ and −∞ are not real numbers)
Can square brackets be used around ∞ and −∞?
{x|2≤x≤4}
If given the interval [2, 4], how would that be written in set builder notation?
(−∞,0)∪(0, ∞)
If given the set-builder notation {x|x<0 or x>0}, how would it be written in interval notation?
False
True or false? There is interval notation for an empty set
[15, ∞) ; (−∞, 0)
Using this picture, show an example of interval notation
{x|x<0} and {y|y≥15}
Using this picture, show an example of set-builder notation
An interval using ∞ or −∞ which indicates that the intervals extend indefinately
What is an infinite interval?
It is used to show the union of two sets
What is the symbol ∪ used for?
[ ]
What type of brackets are used when it is a closed interval (where the point *is* included) ?
( )
What type of brackets are used when it is an open interval (where the point is *not* included) ?
All conditions must be true in order for it to work (do the vertical line test to determine if both conditions are fulfilled). It would look similar to a<x<b when graphed
When *and* is used in set builder notation, what does that mean?
It means that one of the conditions must be true for the inequality to be true
When *or* is used in set builder notation, what does that mean?
Interval Notation: (−∞, ∞) Set-builder Notation: {x|x ∈ ℝ}
Write the interval notation and set builder notation for when the solution is all real numbers
Interval Notation: (-4, -1] Set builder notation: {x|-4<x≤-1}
x is greater than -4 but less than or equal to -1 Write this in interval and set-builder notation
Interval Notation: (−∞, -2]∪(5, ∞) Set builder notation: {x|x≤-2 or x>5}
x is less than or equal to -2 *or* x is greater than 5 Write this in interval and set builder notation
Interval Notation: (−∞, 3] Set builder notation: {x|x≤3}
x is less than or equal to 3 Write this in interval and set-builder notation