3 ms·
> For instance, the two sets {1,2,3,4} and {A,B,C} are such that none is equal to a proper subset of the other. The existence of an injective function is what
by bheadmaster 4y ago
> For instance, the two sets {1,2,3,4} and {A,B,C} are such that none is equal to a proper subset of the other.
The existence of an injective function is what makes subset {A,B,C} a "proper subset" [sic] of {1,2,3,4}, in context of comparing their size.
The terminology could be chosen better, but I think the intended meaning is clear.
- ComplexSystems 4y agoThis 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.
- bheadmaster 4y agoAh, I see. I have't read your comment properly, I guess. That's a fair point, it really seems that comparing sets in general only makes sense in terms of bijections, which makes infinite sets as comparable as finite sets.