I have just started working through a book on higher algebra. I'm just at the beginning, where the authors introduce the notation and talk about the various number systems.(adsbygoogle = window.adsbygoogle || []).push({});

I found this particular paragraph confusing:- "The basic idea in the construction of new sets of numbers is to take a set, call it S, consisting of mathematical objects, such as numbers you are already familiar with, partition the set S into a collection of sets in a suitable way, and then attach names or labels, to each of the subsets. These subsets will be elements of a new number system."

What does the author mean, when he says a "suitable way" here? Does it mean, that I can partition in any way that I find suitable, or are there requirements to be met, for any number system that is constructed by me?

For instance, I'm familiar with the set of natural numbers. So, can I construct S={1,2,3,4,5,6,7,8,9,10} and call it a subset of a new number system? Can I go as far as to say that this subset is the only element of my new number system?

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# Constructing a number system

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