Reading the very interesting 'The German Genius' by Peter Watson and coincidentally the issue of the last post here re infinity, sets and mathematics has surfaced, and so this is really little more than a reiteration of what was already said there. In the mentioned book is told, "Georg Cantor created the theory of sets and the arithmetic of infinite numbers. . . . Cantor made the concept of "set" one of the most interesting terms in both mathematics and philosophy. But it was his next step that took mathematics by surprise(though in truth it was a surprise that no one had noticed this before).The series, 1, 2, 3 . . . n, was an infinite set and so was 2, 4, 6 . . . n. But it followed from this that some infinite sets were larger than others - there are more integers in the infinite series, 1, 2 , 3, . . . n than in 2, 4, 6 . . . n."
That this is nonsense is merely the repetition of the previous post, but here goes again anyway.
There can be no number bigger than an infinite set of numbers since an infinite series is by definition unfinished, never reaches a conclusion, and one thing - here a set of numbers - can only be bigger than another thing if both are complete entities. And so if the series 1, 2, 3 . . . climaxes at the number 175,987 and likewise 2, 4, 6 . . . does not go beyond the same figure, then of course the first set is far bigger than the second. However, obviously enough, we are now dealing here with a finite series of numbers, not an infinite one. There is no permitted climactic figure in the world of infinity, otherwise it is not infinite; and given this, then there is no 'infinite' set that is bigger than another one. An infinite series, tautologically, cannot dwell within the finite boundaries necessary for one set to be bigger than another.