Even in math, though, perfection can be defined, but not achieved.

A (perfect) circle is defined as the locus of points equidistant from a central point. Yet no one has ever constructed a perfect circle.

Irrational numbers are another case. There are numerous infinite series for pi but, even after millions of digits, we don't have an exact value (and never will).

One must be careful. Mathematicians are very careless in their choice of names for mathematical entities. As an example, the solution to the equation:

x² + 1 = 0

was termed an "imaginary" number. There's nothing imaginary about it and it's used widely in many real world applications of math.

They also decided to call numbers equal to their aliquot sums "perfect", e.g. 6 = 1 + 2 + 3. While it's an interesting and fairly rare property, there's nothing "perfect" about it, other than its poorly chosen name.