Determine if the set $\{0.5,1.2,4.7\}$ is a partition of $[0,4.7]$.

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

Determine if the set $\{0.5,1.2,4.7\}$ is a partition of $[0,4.7]$.

Answer: 

The set $\{0.5,1.2,4.7\}$ is not a partition of $[0,4.7]$.

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 $a=0$ and $b=4.7$. First, note that $0$ is not in the set <Sign in to see all the formulas>. Therefore, property 1 does not hold and <Sign in to see all the formulas> is not a partition of <Sign in to see all the formulas>. Since we already know that this is not a partition we do not need to check the second property. We have determined what the problem asked us to determine.