I don't believe that the concept of infinity is ever discussed in mathematics. People usually refer to infinity in two different ways, one as a limit, and another as a range. However, we don't deal with "infinity" as a point. It is not a number. We can only ever know that we do not know infinity at all.

Numbers are studied in abstract algebra as a ring of infinite cardinality. One is natural because it is the multiplicative identity of R* (i.e. any number besides 0 multiplied by its multiplicative inverse, a reciprocal, is 1). Likewise, zero is natural because it is the additive identity in R (i.e. any number added with its additive inverse (negative) numbers, is 0).