This website presents a question that can be only answered by precisely defining "infinity", and then shows an "answer" that just assumes (without proof) a hord

This website presents a question that can be only answered by precisely defining "infinity", and then shows an "answer" that just assumes (without proof) a horde of stuff, including "lim (f * g) = (lim f) * (lim g)". This is not a good way to learn math.