18
votes
4answers
3k views

Why is an image called an “image”?

Given a function $f : A \to B$, the image, denoted by $\operatorname{Im}f$ is the set of all $f(x)$ where $x \in A$. Why do we call this set the image? When was it first used, and what motivated its ...
0
votes
1answer
55 views

Understanding the difference between relations and functions.

$R=\{(1,2),(1,3)\}$ is a relation but not function. The logic for this is that if the first element of every ordered pair must remain different, then it is said to be function. Otherwise, it's just ...
4
votes
3answers
55 views

Concept of a function and Idea of a formula as a function; History of

Enderton Elements of Set Theory, p. 43 (1977, Academic Press), writes: There was a reluctance to separate the concept of a function itself from the idea of a written formula defining the function. ...
3
votes
0answers
30 views

Terminology Regarding Basic Properties of Functions

Is there a cultural difference between saying that a function is 1-to-1 or injective, onto or surjective and a 1-to-1 correspondence or bijective?
11
votes
4answers
180 views

The origin of the function $f(x)$ notation

What are the historical origins of the $f(x)$ notation used for functions? That is when did people start to use this notation instead of just thinking in terms of two different variables one being ...
2
votes
2answers
94 views

why function argument is on right side $f(x)$ rather than on left side as $xf$

Is there an advantage for writing function arguments on the right side as $f(x)$ rather than on the left side as $xf$? The latter looks more natural if we think about it in diagram as $domain ...
3
votes
1answer
59 views

Does the function $f: \mathbb R \to \mathbb R^2, t \mapsto (t^3, t^2)$ have a history?

I heard one mathematician briefly mentioning that the function $f: \mathbb R \to \mathbb R^2, t \mapsto (t^3, t^2)$ is very famous and has a history. Do you know what was meant by that?
1
vote
1answer
55 views

Whats the name of this function?

I read this function in an exercise. It looks quit familiar to me, however I do not know its name. Whats the name of the $\rho_n$ function and who brought it up first?
4
votes
2answers
603 views

History of Functions

I am interested in the history of functions. Why did Euler introduce them? When and why did they become central to mathematics? I know the second question has something to do with the famous ...
4
votes
0answers
42 views

Symbol for function composition [duplicate]

Possible Duplicate: History of $f \circ g$ Choice of symbols can be an indicator of intellectual allegiance. Consider how, back in the day (and before LaTeX regularised things so much!), ...
9
votes
2answers
934 views

Why are even/odd functions called even/odd?

Bit of a silly question, someone told me that the reason even functions are called 'even' and odd functions are called 'odd' is that all (single-variable) monomials with even powers are even functions ...
5
votes
1answer
560 views

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 ...
6
votes
4answers
1k views

History of $f \circ g$

$f \circ g$ is usually interpreted as $f(g(x))$ although, as Google shows, $g(f(x))$ is used frequently too. My question: Does anybody know who was the first mathematician to use this symbol and what ...
10
votes
4answers
764 views

What was the notation for functions before Euler?

According to the Wikipedia article, [Euler] introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical ...
1
vote
1answer
2k views

Proofs of Hyperbolic Functions

I know that functions which are associated with the geometry of the conic section called a hyperbola are called hyperbolic functions. But where on earth did '$e$' come from? I really don't ...
10
votes
2answers
1k views

Why the name 'FACTORIAL'?

Factorial is defined as $n! = n(n-1)(n-2)\cdots 1$ But why mathematicians named this thing as FACTORIAL? Has it got something to do with factors?