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mLine 22:
Line 22: − The real numbers ''do not'' include <math>\infty</math> or <math>-\infty</math> (infinity and minus infinity). The reals contain ''an infinite number of finite numbers.''+
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==Infinity==
==Infinity==
In the standard model of [[Peano arithematic]], the real numbers ''do not'' include <math>\infty</math> or <math>-\infty</math> (infinity and minus infinity). However, there are non-standard models of real numbers which include <math>\infty</math> or include both <math>\infty</math> and <math>-\infty</math>.
There is no largest real number, because you can always make a real number larger by adding 1 (or 137.035 or 6.023·10<sup>23</sup>) to it, and no smallest real number, because you can always make a real number smaller by subtracting from it.
There is no largest real number, because you can always make a real number larger by adding 1 (or 137.035 or 6.023·10<sup>23</sup>) to it, and no smallest real number, because you can always make a real number smaller by subtracting from it.