Convex preferences quasi-concave utility functions, although these are not necessary for the analysis of preferences. Convex preferences In economics, convex preferences are an individual's ordering of various outcomes, typically with regard to the amounts of various goods consumed, with the property that, roughly speaking, "averages are better than the extremes". The concept roughly corresponds to the concept of diminishing marginal utility without requiring utility functions. Comparable to the greater-than-or-equal-to ordering relation formula_1 for real numbers, the notation formula_2 below can be translated as: 'is at least as good as' (in preference satisfaction). Similarly, formula_3 can be translated as 'is strictly better than'
Lens (optics) real object at the location of that virtual image. Likewise, it appears to a subsequent lens as if it were an object at that location, so that second lens could again focus that light into a real image, "S" then being measured from the virtual image location behind the first lens to the second lens. This is exactly what the eye does when looking through a magnifying glass. The magnifying glass creates a (magnified) virtual image behind the magnifying glass, but those rays are then re-imaged by the lens of the eye to create a "real image" on the retina.