The details are given afterwards. In this context, infinity does not exist. In this context, infinity does exist. In the context of a number system. More information is available on this.
Number systems come in many sizes.
Each of these concepts exists provided we look for it in the context of a large enough number system. In the context of a topological space. For instance, the sequence 1.1, 1.01, 1.001, 1.0001, etc. It is important to realize, though, that this topological space is not a number system . This does not really mean what it seems to say.