﻿ oipapio

### functions - Who came up with the arrow notation $x \rightarrow y$?

I read that the arrow notation $x \rightarrow y$ was invented in the 20th century. Who introduced it? Each map needs both an explicit domain and an explicit codomain (not just a domain, as in previous formulations of set theory, and not just a codomain, as in type theory). -- Lawvere and Rosebrugh Sets for Mathematics, 2003...Read more

### elementary set theory - Cardinality of Surjective only & Injective only functions

I'm a college student just beginning to study the very basic of set theory. In studying about Surjective & Injective functions & how they map their domain to their codomain, it came to my mind a question that I really want to confirm:1) Is it possible to build a "surjective non-injective" function with a domain which has a "lower" cardinality than it's codomain?2) Is it possible to build an "injective non-surjective" function with a domain which has a "higher" cardinality than it's codomain?The context of these questions are: This post ...Read more

### Soft Question: Do most mathematicians agree that the function is "the most important concept in all of mathematics"?

Spivak (Calculus, 3e, p. 39) writes: Undoubtedly the most important concept in all of mathematics is that of a function---in almost every branch of modern mathematics functions turn out to be the central objects of investigation.My question is: Would most mathematicians agree with this claim? (I'd like to be able to confidently quote this to high-school students learning about functions and calculus.)...Read more

### percentages - a Function to Push Numbers Away From a Central Number

I'm looking for a function that takes an array of values between a..b (like 0..1) and a central point a < c < b (like 0.5) and a factor (like 2, 3, 4, etc) and pushes all the array's values away from the central point.For example if we have [0.0, 0.25, 0.48, 0.56, 0.87, 0.98] as input to the function, I'm expecting to get something like [0.0, 0.23, 0.41, 0.65, 0.895, 0.9848]. The factor number should be able to control how much the numbers are stretched away from the central point.There are some implementation details like how much should...Read more

### functions - Is my mathematical formulation correct?

I have an input graph as below. I am trying to represent the above pictorial representation in mathematical terms. The above pictorial representation can be viewed as a function from X to P (Y), where P (Y) represents the powerset of Y. P (Y) represents the set of all subsets of Y.Is my above mathematical formulation correct for the given picture?...Read more