Given a 2d plane. With a coordinate system, you can identify an infinite amount of points. That is, the set S of points that lie on the plane has an infinite number of elements.
Now say you only consider the first quadrant of the plane (taking the usual x, y axes as the coordinate system). The set of points Q that lie on the first quadrant still has an infinite number of elements.
However, intuitively speaking, |S| > |Q|.
The same scenario can be done with a number line and the positive number line.
I don't know much about infinities mathematically. Is this mathematical, or just misleading intuition?