During studying set cardinality, I came across on this exercise:
$$2{}^{\aleph_0}2 = {}^{\aleph_0}2 + {}^{\aleph_0}$$
I understand that ${}^{\aleph_0}2$ is just $2^{\aleph_0}$ written in this way, at least previous text implies it. But I am really confused about what $^{\aleph_0}$ is supposed to be as there is no explanation for it whatsoever. There is a solution to the excercise, but it uses the same notation and therefore I do not understand it, even if it's quite short.
I think it's some typographical mistake, but having only brief background in cardinality, I can't figure out what the equation means. I bet it's either meant to be $2^{\aleph_0}$ or simply ${\aleph_0}$. Could you please find an explanation of this typo or post a meaningful version of the equation?
P.S. The textbook is in Slovak, so I won't post the solution here. Though I will translate it if it's necessary.
I have concluded that the stated equation really is a mistake in the textbook and that the intention was to write $2{}^{\aleph_0}2 = {}^{\aleph_0}2 + {}^{\aleph_0}2$ as Mr. Caicedo pointed out.