Is there another convincing way, other than the one orginally used by cantor, of prooving that there exists infinitys greater than alpha zero? I ask because cantor's proof seems a bit shaky to me, at least the way I've read it. I hear that there is some discontent amongst top maths dudes circles with it as well. I wonder that the reason why that big conjecture about infinitys existing between alpha zero and one is undecidable is because there is only one infinity, therefore invalidating all the concepts which different size infinitys rely upon. There maybe some infinite sets which are uncountable, but maybe that doesn`t imply more than one infinity.