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Precisely as many angels as there are whole numbers, or exactly as many as the quantity of numbers you can count between 0 and 1 (0.5, 0.2341, etc).
The original context of the question was more about if angels and the afterlife were physically manifest or intangible, and early thinking about how infintesimals work.
But there are more numbers between 0 and 1 then there are whole numbers. So are the countable many angles or uncountably many?
I specified countable to keep them in the same class of infinity. :) not about to make that mistake when bringing pedantry to a silly fight. .
Since it's implied that they have names, I'm going to use that as my argument for there being a countably infinite number. If you want to argue that only certain special angels have names, like Michael or π, then I'd say they're uncountable.
If you wanted to argue that omnipotence means a deity could defy logical restrictions and allow contradictory truths to coexist, then I'd say I'm far too sleepy for that discussion but I love where you're heads at. :P