Evolution of the Function Concept: A Brief Survey

Pointfree expression and calculation: from quantification to temporal logic

“…A historical overview is found in [57]. Here we only consider the question: what should the concept of a function incorporate and what is better avoided?…”

“…Typical definitions are found in [49,51,75] and discussions in [57,76]. An observation: most definitions do not define a function but a function from a set X (in)to a set Y (up to set naming)!…”

Growing mathematical objects in the classroom – The case of function

“…This process began at the turn of the eighteenth century, when Leibniz initiated the use of the word function in the geometric context and Johann Bernoulli, possibly as a result of his correspondence with Leibniz (1694-1698), proposed a definition that portrayed function as an algebraic construct: one calls here Function of a variable a quantity composed in any manner whatever of this variable and of constants (Johann Bernoulli, 1718; after Kleiner, 1989). While Bernoulli's focus on algebraic symbolism was only implicated (variables and constants are to be understood as letters used in particular mathematical ways), it became quite explicit in Euler's reformulation of 1748, which identified function with analytic expression (A function of a variable quantity is an analytical expression composed in any manner from that variable quantity and numbers or constant quantities; Euler 1748; after Kleiner, 1989).…”

A Note on the Relation Between Formal and Informal Proof

“…18 See Pedersen (1974). 19 Euler, like other 18th-century mathematicians, did not distinguish between the concepts function, and continuous function (Kleiner 1989). 20 See Carnap (1950), pp.…”

“…Discussions of whether there are species or just individuals, and questions about the stability 17 Euler, Introductio in Analysin Infinitorum, 1748. The quotation is from Kleiner (1989). 18 See Pedersen (1974).…”