Real Number and intervals
Real Number Line
: can write 
or R (you can add a superscript 1 to emphasize this is first Euclidean space, either notation is fine), is the real number line. close all;
figure();
x = linspace(-10,10);
line(x,0*ones(size(x)))
set(gca,'ytick',[],'Ycolor','w','box','off')
ylim([-0.1 0.1])
pbaspect([4 1 1])
grid on
Non-negative numbers
In many economic problems, we have to restrict ourselves to numbers greater or equal to zero.
- We can not consume from negative numbers of apples
- We can not produce with negative labor and capital
- We would be infinitely unhappy (die) if there is zero consumption in a year
We can use the following notation to define the set of non-negative real numbers:
, some authors use 
instead of 
And use inequality sign to define the set of real numbers greater than zero:
, some authors use 
instead of 
close all;
figure();
x = linspace(0,10);
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
