Lukas' Notes

Definition

Infinity

Infinity denotes non-finiteness. For a set, it means that no finite number counts all its elements; for growth towards , it means eventually exceeding every finite bound. The symbol is not a real number.

Potential infinity concerns indefinitely extendible finite stages; actual infinity treats an infinite totality as given at once.

Extended real arithmetic

Adjoining two symbols gives the extended real line . For finite , addition and multiplication are commutative and satisfy

The expressions , and are undefined in this convention.