ABSTRACT
This chapter introduces certain concepts that play a role in virtually every branch of mathematics. Although there are not very many of them, basically, sets, relations and functions, learning them for the first time can be difficult: partly because they are abstract, and partly because they are unmotivated. Probability theory starts with counting because the cardinality of an event that the readers might be interested in divided by the cardinality of the finite sample space is defined to be the probability of that event, assuming all elementary events to be equally likely. The Boolean operations are ubiquitous, being particularly important in probability theory. All of mathematics can be developed within set theory, and this would suggest that set theory really is the foundation of mathematics. But in 1945, Samuel Eilenberg and Saunders Mac Lane introduced a new approach to mathematics, called category theory, in which the notion of function is taken as basic rather than that of set.
