descriptions of relationships
Mathematicians are interested in describing the world in very general terms. They don't just want to describe the relationship between me and my cousin, or you and your cousin. They want to describe in very general terms the relationship between anyone in the world and their cousin.
Question: What would a general description be of the relationship between a person and their cousin? Try writing this description out. (Once you’ve tried to work it out yourself, see Answer 1, bottom of page)
You may have come up with your own perfectly good definition, but for now, let's go with the description "A person's cousin is the child of one of their parents' siblings"
This sort of description is very powerful, because it can be applied to anyone in the world. However, as perhaps you can see from the above exercise, such a description can also be confusing and hard to use or understand. That's because it's much easier for humans to think in terms of specific examples rather than in general or abstract descriptions. Using general descriptions is another mathematical skill that takes practice. It often helps to re-read the description several times. Why not try it out?:
"A person's cousin is the child of one of their parents' siblings"
Answer 1: There’s more than one possible answer. One possible answer would be “A person's cousin is someone who is the son or daughter of a brother or sister of that person's mother or father.” Another possible answer would be “A person's cousin is the child of one of their parents' siblings.”