I think the distinction is really between "A given infinite set" and "every conceivable thing". It's a common fallacy to equate one infinity with any other infi

I think the distinction is really between "A given infinite set" and "every conceivable thing". It's a common fallacy to equate one infinity with any other infinity, and therefore any given infinity must contain all things. This fallacy is very neatly encapsulated by the phrase >If there are infinite numbers, and all numbers have a name, then there must exist a number called door