Determine if the set $\{-20,-19,-10,-5.5,-2,-1,0\}$ is a partiton of $[-19,0]$.

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Lesson Parent: 
Integration II: Partitioning the x-axis.
Problem: 

Determine if the set $\{-20,-19,-10,-5.5,-2,-1,0\}$ is a partiton of $[-19,0]$.

Answer: 

The set $\{-20,-19,-10,-5.5,-2,-1,0\}$ is NOT a partiton of $[-19,0]$.

SAMPLE SOLUTION

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Solution: 

Recall that a partition of $[a,b]$ has the following properties:

  1. It includes the numbers $a$ and $b$.
  2. The other elements of the partition are between $a$ and $b$.

We typically write the partition such that <Sign in to see all the formulas>. If we do then both properties are automatically satisfied.

In this problem $a=-19$ and $b=0$. Let's go through the properties:

  • The set does include $-19$ and $0$.
  • Property 2 does not hold because $-20$ is not between $-19$ and $0$.

Therefore, the set <Sign in to see all the formulas> is not a partition of <Sign in to see all the formulas>.