This re-instated what passes for faith in humanity

[wakim]

If you're going to talk  about "infinity" then I'm afraid you have no alternative other than to understand something about how it is defined in mathematics; otherwise what you say is liable to degenerate into meaninglessness, and what seems counter-intuitive or contradictory may just turn out to be an unexpected property of infinite numbers.
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I won't quibble; I grant this.

For example, if I interpret you correctly, you don't like the fact that for every  natural number there is a natural number which is larger than it  (the natural numbers  have  'no upper limit') yet  there is a number that is larger than every natural number (the natural numbers are 'bounded'). That isn't a contradiction, however; that's how it works.
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You are correct. How one can resolve this contradiction, despite your friendly reassurance, I do not see.

Exactly what Cantor did was to show that in a precise way there are different 'magnitudes of infinity'...  and that, for example, the real numbers are 'more infinite' than the integers or the rational numbers.
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I am not yet inclined to grant differing flavors of infinity - for better reason than simply that I can recall playground arguments that ultimately devolved into meaninglessness once infinity was allowed to be treated as a number of finite magnitude: "Uh-huh." "Nuh-huh." "Uh-huh, uh-huh." "Nuh-huh, nuh-huh, nuh-huh." "Uh-huh infinity!" "Nuh-huh infinity plus one!"

I will grant, however, that if one defines "infinity" to mean something different, then naturally different conclusions will follow from that. Perhaps, until I have had the opportunity to study set-theory and thus engage its premises and conclusions more intelligently, it would suffice to return to the original question that sparked this digression and ask whether such an understanding is an application of more precision to the question than it merits?

The question was, if I recall, whether a set than contains some quantity of elements, whether infinite in magnitude or not, could exist that did not contain a first element? - "Thus, how if one claims a set of infinite items, can it not contain a first item?" The point of contention that you drew was over "So what is infinite can be larger than what is infinite? [Isn't there] contradiction in stating that a thing may be larger than itself?" This point seems incidental to the question, and I don't see why, if contested, it may not be discarded without loss to the cogency of the argument.

Perhaps you'd be inclined to grant that if one accepts infinity to mean "immeasurably great, unlimited, boundless, endless" that the point of contradiction is valid? and, in general, that a thing may not be larger than itself? and, further, ascribe the use of ambiguous language that failed to encompasses Cantor's divisions of the infinite (and thus inadvertently referred to many things as if they were only a single thing) as evidence of my finitude and not the fallacy of the argument?