From Middle English real, from Old French reel, from Late Latin reālis (“actual”), from Latin rēs (“matter, thing”), from Proto-Indo-European *reh₁ís (“wealth, goods”). Doublet of realis. In modern times, likely strengthened by or conflated with the use of the prefix re-, analyzable as re- + -al.
(economics) Relating to the result of the actions of rational agents; relating to neoclassical economic models as opposed to Keynesian models.
(mathematics, of a number) Being either a rational number, or the limit of a convergent infinite sequence of rational numbers: being one of a set of numbers with a one-to-one correspondence to the points on a line.