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Section 8.2 An Abstract Look at Intervals
First, we can consider an interval in geometric terms as the point
\((\underline{a},\overline{a})\) in
\(\R^{2}\text{.}\) Some examples are:
Figure 8.2.1. And since for intervals
\(\underline{a}\leq \overline{a}\text{,}\) then all intervals can be represented as points on or above the line
\(y=x\text{.}\) All thin intervals are on the line
\(y=x\text{.}\)
Note also, that if we think of intervals in this way that addition is the same as vector addition. That is, as an example
\begin{equation*}
[3,4] + [-2,1] = [1,5]
\end{equation*}
Question: Is the set of all intervals with addition and scalar multiplication defined as ??? a vector space?
