A function in mathematics[^1] is a relation between a value in a domain and a value in a codomain across a range. In programming terms, this means that mathematical functions are single-arity and pure. In other words, they take a single value and, given the same value, always produce the same output.
In maths[^1], a real number is a number that can be used along a number-line. They are called real numbers to differentiate them from imaginary numbers. The set of all reals is denoted with \\mathbb{R}.
In maths, for a given function, it can be said to operate 'over' a set in the case that its domain and codomain are in the same set. For example the function f : \\mathbb{R} \\rightarrow \\mathbb{R} could be said to be a function over reals.
In maths, a tuple is a n sized group of mathematical objects. For example, a 2-tuple is 2 mathematical objects and a 3-tuple is 3 mathematical objects.