Operations of a Post Worker
An exposition of the paper "Finite combinatory processes-formulation 1" by Emil Post (1936), where he presents a model of computing based on operations on a symbol space determined by a given set of directions. Post hypothesizes, but does not prove, that his concept of computability is logically equivalent to the concept of recursion in the sense given by Gödel and Church. This paper was published the same year that Turing published his famous paper "On Computable Numbers, with an application to the Entscheidungsproblem", where he introduces the concept of computability, also logically equivalent to recursion, that now bears his name.
Dedekind: Addition of Reals
An exposition of the addition of real numbers defined as cuts as presented in Dedekind's "Continuity and irrational numbers, in essays on the theory of numbers" (1872). The proof that the addition of two cuts determine a unique cut in the case of the sum of a rational and an irrational number. This shows how the reals inherit the additive structure of the rational numbers.