Apologists often claim that actual infinites are logically impossible. One of the arguments which they utilize to support this claim deals with subtracting quantities from infinite quantities. One example of this comes from Blake Giunta’s Belief Map:
Infinity minus an infinity yields logically impossible scenarios. Notably, one can take away identical quantities from identical quantities and arrive at contradictory remainders.
On the face of it, this claim appeals to our intuitive understanding of subtraction. If I were to claim that there exists some Integer, , such that and , then we stumble upon the contradiction that . Subtracting identical quantities from identical quantities should yield identical results.