$\infty$ (Infinity) is not a number, but infinity is considered to be defined, right?
There are expressions in mathematics such as: $\frac x0,0^0, \frac\infty\infty,$ which are not defined because they do not have a certain place on any domain, and sometimes because there is no single value that satisfies all functions yielding such expression in a limit.
How can infinity be defined?
Maybe the argument would hinge on how 'defined' is defined?
Perhaps this requires a circular(infinite) argument?
Or is my assumption that infinity is considered to be defined; false?