Doesn't that mean the interval from 3 to 3, not including 3?provide further context
The statement that \(\displaystyle (a,b)\) is an open interval in the set of real numbers means that \(\displaystyle a~\&~b\) are two real numbers and \(\displaystyle a<b\).Doesn't that mean the interval from 3 to 3, not including 3?
The statement that \(\displaystyle (a,b)\) is an open interval in the set of real numbers means that \(\displaystyle a~\&~b\) are two real numbers and \(\displaystyle a<b\).
\(\displaystyle (a,b)=\{x\in\mathbb{R}: a<x<b\}\)
Anyone who can count knows that \(\displaystyle a=a\) so \(\displaystyle (a,a)\) does have two real numbers therefore by definition is not notation for an open interval.and thus \(\displaystyle (a,a) = \{x \in \mathbb{R} : a < x < a\} = \emptyset\)
But [a,a] is.Anyone who can count knows that \(\displaystyle a=a\) so \(\displaystyle (a,a)\) does have two real numbers therefore by definition is not notation for an open interval.
But [a,a] is.