This is exactly what I wrote about in my second paragraph, isn't it? The intended meaning is not clear, because this definition again makes the set of naturals

This is exactly what I wrote about in my second paragraph, isn't it? The intended meaning is not clear, because this definition again makes the set of naturals the same size as the set of squares. > On the other hand, we can say that although {A,B,C} is not equal to any proper subset of {1,2,3,4}, it is in bijection with a proper subset, such as {1,2,3}. Although this is true, if we use this definition of "the same size as," we again get that the naturals are "the same size as" the set of all squares.