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> Infinity is neither a number nor a quantity. It's not a number, because you can't get there by counting.

That's an oddly narrow implied definition of "number" which, as well as infinity, would exclude everything other than the natural numbers. Maybe it extends to the integers, if you use an unusually generous definition of "counting". But it certainly excludes non-integral rationals, and, a fortiori, all irrationals from the set of "numbers".

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Maybe "count" is too restrictive depending on how you think of counting. Substitute "reached" or "located" if you like. As another comment here says (paraphrasing) if a real can't be named, is it even a thing? I'd say any real that can be named can be "counted to" from another real that's arbitrarily close to it. If that's still too restrictive, then for any real that can be named, I can point to a segment of the number line and say "It's roughly, round about... there." Can't do that for infinity, again, because it's not a number.

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