The concept of infinity and its use is one with different meanings through the centuries within various contexts reflecting mathematical historical development. This development is scarcely clear to pupils during school time and rarely stressed in teacher education although it offers a lot of potential to understand mathematics. The field of arithmetic is one example in which to study infinity within a range that student teachers are able to understand and that is useful for and in their future teaching. The paper focusses on the potential of this concept within the arithmetic field using an original article of Cantor and on examples, also from Hilbert, that stress different counting methods and various illustrations of infinity.