We have described a human approach to numbers, namely, mapping groups of a certain size to the number as well as to each other.
But this feels a little unspecified even if we all know what words like four means. Maybe it would be nice to have some canonical example to represent the concept of four.
Once we establish that, we then can ask about making sense of negative numbers and fractions just using the positive numbers. Again, we know how they should behave, but how do we put all of that on a firm foundation?
We will explore these ideas here. It is safe to skip this chapter if you are cool with the numbers as is. But, if you want a better viewpoint on what a number is, please read on. This chapter will explore these ideas, going into some details, but leaving other details to the proof section.