Because unbounded includes infinity, oscillation, piecewise function and many other situations.

For example, the functions 1, -2, 3, -4, 5, -6, ..., 2n+ 1, -2n, ...

This is an unbounded quantity, but it is not infinite. It will oscillate.

There are different definitions of infinity in set theory. German mathematician Cantor proposed that the number of elements (cardinality) corresponding to different infinite sets has different "infinity". The sum of two infinite quantities is not necessarily infinite, the product of bounded quantity and infinite quantity is not necessarily infinite (for example, the constant 0 is a bounded function), and the product of finite infinite quantities must be infinite.