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But I don't think the same rule applies for subtraction. Multiplication and addition, yes it is infinity but the subtraction and division of infinity are different.
To try to explain it, imagine the infinite space that we live in. Now if you were to not include the milky way as part of space, space would still be infinite.
Or if you had an unlimited amount of money, you could divide it amongst your friends, and you, and your friends would still have an unlimited amount of money.
But even dividing infinity by infinity is very strange. Hilbert's paradox of the Grand Hotel, shows that if you had an infinite number of guests, and an infinite number of rooms for them to fit in, then the hotel will never be full.