We describe how to write an algorithm which results in sorting a list into ascending numerical order.
We begin by formally defining a limit. We then show, step-by-step, how to prove that the limit of a function at a given point is equal to a given value.
We show, step-by-step, how to show that a mapping is a bijection. We do this both directly, and by finding an inverse function.
We show, step-by-step, how to prove that a relation is an equivalence relation. We then find the equivalence classes and the corresponding partition.
We show, step-by-step, how to use induction to prove that an equation holds for all natural numbers.