Interval Notations and Examples
When we look at the problem facing a household, we often have to restrict the choice set for example to an interval.
Closed Interval
For example, if x is hours working, perhaps the household has to work at least a hours and up to b hours, so his choice is between a and b hours inclusive.
The interval that is inclusive of both endpoints is called a closed interval (note the square brackets):
- closed interval:
Open Interval
In general, an open interval is defined as (Note here we use parenthesis, not square brackest) :
- open interval:
Half Open and Half Close Interval
We can also hafl half open intervals:
- half open (half closed) interval:
- half open (half closed) interval:
Graph
If you were to graph an interval, you can draw an empty circle at either end of an interval that is open, and a solid circle if it is closed at that end.
close all;
figure();
x = linspace(-1,5);
line(x,0*ones(size(x)))
set(gca,'ytick',[],'Ycolor','w','box','off')
ylim([-0.1 0.1])
xlim([-10 10])
pbaspect([4 1 1])
grid on
