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