One cannot say infinity exists if we have no means of defining it; the concept of infinity is impossible for the human brain to understand because the thought that something—-Anything!—can simply go on forever without end is an abstract theorem that is innately incomprehensible; we cannot comprehend infinity since life offers us no frame of reference with which to envision it. Thus, one cannot use infinity as a mathematical answer and then in the next breath say that infinity is a concept and not an actual number. The field of mathematics is predicated solely on the usage of arbitrary numbers and numbers alone; introducing vague concepts like infinity as the answer to mathematical riddles is not only illogical but, more importantly, dishonest. And then esteemed mathematicians and logicians mix in the absurd thought that there are different levels of infinity i.e. that certain infinities are greater in stature than other “lesser” infinities, and this subject next crosses over the boundary separating logic from zany illogic, rationality from irrationality, possibilities from blatant impossibilities. How could such a crazy thing even be possible? How could one set of numbers go on forever, but then there is another set of numbers—numerous sets actually, if smug mathematicians are to be believed—that goes on even beyond that…..beyond forever? Yes, you heard me right: Beyond FOREVER!!! I don’t think so. C’mon, if infinity is impossible for human beings to comprehend, then some theoretical entity greater than a “standard” infinity is utterly preposterous and takes a giant leap into the realm of disjointed nonsense and gobbledygook. Impossible to reconcile logically, and definitely impossible to reconcile with anything in everyday life. At this surreal juncture the concept of infinity becomes little more than a semantic hot potato with no real meaning and no actual tethering to the real everyday world we mortal human beings inhabit.
Fred's Soapbox 