Something $= \infty$ Let $\alpha$ be the number of solutions of certain equation. I want to say that the number of solutions are infinite. Can I write $\alpha = \infty$ or is it wrong to write that?

What you have written is not wrong, but the notation is really uncomfortable. By uncomfortable I mean to say that what you are representing is the cardinality of a set which contains solutions to a certain equation . Now as Crostul says there are many kind of infinities and someone looking at it might not (countably infinite, uncountably infinite) understand what you are trying to convey
