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\({R^1 }\) : can write \(R^1\) 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
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:
\({R_{\ge 0} }\equiv \lbrace x\in R:x\ge 0\rbrace\), some authors use \({R_+ }\) instead of \({R_{\ge 0} }\)
And use inequality sign to define the set of real numbers greater than zero:
\({R_{>0} }\equiv \lbrace x\in R:x>0\rbrace\), some authors use \({R_{++} }\) instead of \({R_{>0} }\)
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