Mathematicians were very cautious using the concept of infinity and many rejected the concept, abolishing it from mathematics. The first real improvement towards a mathematical definition of infinity is due to somebody by the name of Bernard Placidus Johann Nepomuk Bolzano.

In his work "Paradoxes of the Infinity" (1840) he established the first building blocks of what we know today as set theory, introducing the very concept of set and one-to-one (injective) mappings, (surjective) maps and bijective functions.

In order to understand these concepts, we suggest the following entries from Wikipedia:

1. Function.
2. Injective Function.
3. Surjective Function.
4. Bijective Function.
5. Cardinality.