I can recall proving to my students (with my tongue firmly planted in my cheek), that the speed of light decreases as the age of the universe increases. The "proof" goes like this:

Assume that the speed of light is an unknown function of R, the radius of the universe, and A, the age of the universe.

Then c = f(R, A) . Now change units so that distances get multiplied by x and time gets multipied by y

... like changing from feet to metres and seconds to years.

Since c = distance/time, we'd get (x/y)c = f(xR, yA). Now choose x = 1/R and y = 1/A and get (A/R)c = f(1,1) or c = f(1,1)R/A.
Whatever the function f, f(1,1) is a constant, so c decreases as A, the age of the universe, increases.

The students we impressed
... until I repeated the proof with R the radius of a gumball and A the age of my daughter.

Perhaps I shouldn't have dismissed this proof so readily :^)