I made a nice little discovery yesterday:

a function being injective and a function being constant are kind of opposites of each other - intuitively this makes sense as "every output is unique" vs "every output is the same", but you can get to it symbolically as well:

injectivity:
for all a, b: a ≠ b → f(a) ≠ f(b)

constantness:
for all a, b: a ≠ b → f(a) = f(b)