Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I am having difficulty interpreting the definition of addition provided in Hardy' Course of Pure Mathematics.

(i) Addition. In order to define the sum of two numbers α and β, we consider the following two classes: (i) the class (c) formed by all sums $c = a+b$, (ii) the class (C) formed by all sums $C = A+B$. Plainly $c < C$ in all cases.

α and β are the points of two sections with a and b being the lower classes and A and B being the upper classes.

In case I left out a critical detail, here is the link to an online copy. The page number is 18.

http://www.gutenberg.org/files/38769/38769-pdf.pdf

My confusion is how to interpret $c=a+b$ and $C=A+B$. What I don't understand is how you can add two sections.

share|improve this question
add comment

1 Answer

up vote 2 down vote accepted

In Hardy's book, we are actually adding representatives of the lower and upper classes respectively, not the sections. When we consider the new classes formed, we end up with a new section, which is how we define $\alpha+\beta$. Since the lower case letters represent members from the lower class (equivalently, the members less than the corresponding Greek letter), it makes perfect sense that $c<C$. I hope this helps!

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.