# Seminar in Abstract Mathematics Bulletin

### Special achievements of students

## 2011

Ms Grobler (third year Biomathematics student) finds a "visual method" for deciding transitivity of a relation, which is based on "matching columns" in its graph.

Mr Weighill (third year Engineering student) independently proves the well-known Cantor-Bernstein Theorem which states that if two sets can be injectively mapped into one another, then they are bijective. His proof first constructs a bijection on the partitions of the given sets (where each element of the partition is the "chain" obtained by repeatedly applying the composite of the given injections), and then lifts the bijection to the original sets.

## 2012

Mr Van Niekerk (second year Mathematics student) proves that in a group, if the number of elements x satisfying xx=1 is finite, then it is either equal to 1 or is even.

Mr Van Niekerk (second year Mathematics student) independently discovers the well-known proof of the Cantor-Bernstein Theorem.