8
votes
0answers
393 views

Has anyone pursued Frege's idea of numbers as second-order concepts?

Gottlob Frege was a pivotal figure in the history of mathematical logic. He gave an analysis of numbers that proceeded along roughly the following lines, in his books "The Foundations of Arithmetic" ...
14
votes
3answers
1k views

Who introduced the terms “equivalence relation” and “equivalence class”?

Consider that the question does not concern the origin of the ideas of equivalence relation and equivalence class. It exactly concerns the origin of the terms "equivalence relation" and "equivalence ...
5
votes
1answer
629 views

Why do mathematicians prefer one definition over the other when they both define the same concept?

Here is a basic, though very important, example: Hilbert takes as primary the notion of “congruence” (or “equal”) between segments. His first axiom of congruence “requires the possibility of ...
3
votes
0answers
401 views

sine and Archimedes' derivation of the area of the circle

The elementary "opposite over hypotenuse" definition of the sine function defines the sine of an angle, not a real number. As discussed in the article "A Circular Argument" [Fred Richman, The College ...
3
votes
2answers
433 views

Evolution of the Mapping/Function Concept

Hello! I'm looking for a survey (of the history) of the concept of mapping/function. How the concept was evolving. Especially I'm interested in what it turned into during the last 50 years. So ...
10
votes
1answer
1k views

Up-to-date version of Principia Mathematica?

Background: I found this interesting translation of Godel's On formally undecidable propositions of Principia Mathematica and related systems I that, along with translating it into English, uses more ...
4
votes
3answers
1k views

Dedekind's theorem

In "Was sind und was sollen die Zahlen?" Dedekind gives a noncircular proof of the statement that a set is finite if and only if it cannot be put in bijective correspondence with a proper subset.  By ...