Meaning of irrationality of a constant

Question

What is the meaning, when it is the irrationality of a constant?

I understand that irrational means can't be represent as a fraction.

Answer 1

We can define constants in many ways. Sometimes it is not clear whether the constant is rational or irrational. An example would be $$c=\sum_{i=1}^\infty \frac 1{i^2}$$
Once I prove convergence, this is a fine definition of $c$. From this definition, it is not obvious whether $c$ is rational or irrational. As there are so many more irrational numbers than rational numbers, we would be prone to guess that $c$ is irrational because we don't see any reason it should be rational. In this case we know it is $\frac {\pi^2}6$ which is irrational.