## Chapter 1THE REAL VARIABLE

‘In dem days dey wuz monstus fon’ er minners.’

JOEL CHANDLER HARRIS, *Uncle Remus*

### 1·01. The relation of mathematics to physics.

The simplest mathematical notion is that of the number of a class. This is the property common to the class and to any class that can be matched with it by pairing off the members, one from each class, so that all members of each class are paired off and none left over. In terms of the definition we can give meanings to the fundamental operations of addition and multiplication. Consider two classes with numbers *a*, *b* and no common member. The sum of *a* and *b* is the number of the class consisting of all members of the two classes taken together. The product of *a* and *b* is the number of all possible ...