0
votes
0answers
49 views

About Kernel and the coimage of a function

Introduction I was serching for a concept of "equivalence relations" induced by an arbitrary function in a "natural" way and I found the concept of Kernel. But I'm not sure that I understand it and ...
0
votes
1answer
68 views

What are functions with the property $f(f(x)) = x$ called?

Do functions which, when composed with themselves, are equivalent to the identity function (i.e. functions for which $f(f(x)) = x$ in general) have a name and if so, what is it? Additionally, am I ...
0
votes
2answers
38 views

What is called the property of function that it does not change value when you transform arguments.

My question is probably rather simple, but I cannot find appropriate name or am too stupid to find a definition of such property. I'd like to give an example: $f({\bf r}_1, ..., {\bf r}_N, ) = ...
3
votes
0answers
28 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?
2
votes
1answer
271 views

into function vs injective function

In many mathematical books that I have read and from lectures from professors, the words 'into' and 'injective' were used interchangeably, but in Patrick Suppes book Axiomatic Set Theory he gives a ...
2
votes
2answers
88 views

What do you call a function with the property $f(-x)=-f(x)$?

What is this property called? The domain and codomain of the function can be for example $\mathbb Z^n$, $\mathbb Q^n$ or $\mathbb R^n$ ($n>0$), potentially excluding the $0$ point. Examples: ...
0
votes
1answer
35 views

Adding together curves or shapes to approximate something more complex

I'm looking for proper terminology / references for the following sort of problem: Say we have some one-dimensional curve like $y = 10$ defined over the real valued domain $[0,1]$, and we ask, how ...
1
vote
0answers
24 views

Terminology for functions with $F(a,a,\dots,a) = a$

Is there a commonly used way to call functions $F : \mathbb{R}^n \rightarrow \mathbb{R}$ such that if $x \in \mathbb{R}^n$ and $x_i = a$ for all $i\in \{1,\dots, n\}$, $F(x) = a$ ?
1
vote
2answers
77 views

Notation and terminology for functions, interpreting $f(y)$

It seems to me there are two different interpretations of a symbol $f(y)$. I will explain what I mean: Suppose I have a function $f(x) = x$. (I took the identity map to have a simple example). Also ...
1
vote
0answers
22 views

What can I use as the generic term for “a function that is composed with another”?

Suppose I am talking about the composition $g \circ f$ (or more generally $f_n \circ \cdots \circ f_1$). Is there a generic term for the functions $f$ and $g$ (the functions $f_i$)? "Compositand"?
0
votes
0answers
16 views

Definition of Range as Minimal Interval Containing Codomain

I am studying continuous functions where the domain is some interval (which may or may not be bounded, closed, etc). I am thinking about how continuity is related to other function properties, ...
1
vote
2answers
45 views

Matrix with Functions as Entries

What do we call a matrix with functions as entries? $$\textbf{f(x)}=\begin{bmatrix} f_{11}(x) & f_{12}(x) \\ f_{21}(x) & f_{22}(x) \end{bmatrix} $$
0
votes
1answer
56 views

What is the terminology for this type of order-preserving function?

As I roughly know, a function $f$ in $\mathbb{R}$ is called order-preserving if $f(x)>f(y)$ for $x>y$, $x,y \in \mathbb{R}$. May I ask, if anybody knows the terminology for two functions $f$ ...
0
votes
0answers
24 views

Is there terminology to describe this type of function equivalence?

I have a binary vector, for simplicity of explanation, it contains +1's and -1's. Next I have a starting value, for example 5. As I iterate over the vector, my function takes my current value and adds ...
2
votes
0answers
38 views

Inverses of two argument functions with respect to one argument

Consider a function $f : A \times B \to C$ and two inverses, each with respect to one argument; i.e. $g$ and $h$ defined such that $f(x,y)=z \iff g(y,z)=x \iff h(z,x)=y$. A simple example is addition: ...
1
vote
2answers
104 views

Partial functions - where can I learn more about this (heuristic, informal) system of conventions?

Is there a name for the following (heuristic, informal) system of conventions for dealing with partial functions and undefined expressions? I'd like to know whether it has any undesirable quirks that ...
1
vote
1answer
51 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?
6
votes
4answers
118 views

The limit of $f$ or the limit of $f(x)$?

I have read before that $f$ denotes the function $f$ whilst $f(x)$ denotes the value of the function $f$ at $x$. What is right? To say that the limit of $f$ as $x$ tends to $a$ is $L$ or to say that ...
1
vote
4answers
69 views

What is an odd function?

I'm reading this term (odd function) in my numerical analysis book, but I have never heard of this. What does it mean that an function is odd ?
1
vote
1answer
119 views

The bijective property on relations vs. on functions

I recently encountered what seems to me like an inconsistency in the usage of the term bijective. This is pretty basic stuff, but it somehow never occurred to me before. I'd like to make sure I'm ...
3
votes
1answer
80 views

One-to-one mapping vs one-to-one correspondence

Does the phrase "one-to-one mapping" mean the same thing as "one-to-one correspondence?" I know that the latter refers to a bijection. Does the former refer to an injection (i.e. it is the same as ...
1
vote
0answers
38 views

Condition for being 'injective in each variable separately'

Is there an established term for a function on a product set that is not injective but is injective with respect to each argument individually? The motivating example is the canonical projection $\pi: ...
2
votes
1answer
80 views

Terminology for $\phi(xy)=\phi(x)\phi(y)$

I have a model which contains a function $\phi:{\mathbb R}_+ \rightarrow {\mathbb R}_+$ that satifies: $$\tag{*}\phi(xy)=\phi(x)\phi(y)$$ for all $x,y\in{\mathbb R}_+$. In Number Theory there is a ...
6
votes
3answers
158 views

Unambiguous terminology for domains, ranges, sources and targets.

Given a correspondence $f : X \rightarrow Y$ (which may or may not be a function) I generally use the following terminology. $X$ is the source of $f$ $Y$ is the target $\{x \in X \mid \exists y \in ...
19
votes
4answers
390 views

“$f$ is a function from $A$ to $B$” vs. “$f $is a function from $A$ into $B$”?

When we say that $f$ is a function from $A$ to $B$ is this different from saying $f$ is a function from $A$ into $B$ I know what injective ("1-1"), surjective ("onto"), and bijective ...
2
votes
1answer
70 views

Is there a name for the function $(1 - e^{ct})/(1 - e^{c})$?

$$f(t) = \frac{1 - e^{ct}}{1 - e^{c}}$$ This is a function which is somehow a streched exponential which is zero at $t = 0$, and one at $t = 1$, where $c$ determines the curvature (with $c = 0$, it ...
5
votes
1answer
100 views

Is the variant direct image mathematically significant?

Preimages have the property that for an arbitrary function $f : X \rightarrow Y$ and all $B \subseteq Y$ it holds that $$f^{-1}(B^c)=[f^{-1}(B)]^c.$$ However, the analogous statement for direct ...
3
votes
0answers
51 views

What's the mathematical field called where functions create and delete functions?

Motivation In the field of modular, reconfigurable robotics there are some groups which use term rewriting, or specifically graph rewriting to describe the reconfiguration process of the modular ...
1
vote
5answers
586 views

How do I find the image of the functions $y=2$ and $y = 2x - 6$?

The function is $y=2$, the domain is just 2? And the image of it? I don't think I quiet understand what the image of a function means, the domain is all values that it can assume, correct? Could you ...
1
vote
1answer
1k views

Definition of correspondence

A one-to-one correspondence is an alternative name for a bijection between two sets, but to what does the term 'correspondence' alone refer? As far as I can see, it seems to be another term for ...
1
vote
1answer
46 views

Limit of a seqence $\{f_n \}_{n\in \mathbb N}$ of functions?

I don't really know how mathematicians talk about this concept. I try to explain better what I mean with limit of a sequence of functions: Given a countable set of functions $\{f_n \}_{n\in \mathbb ...
1
vote
2answers
63 views

correct name of mathematical property

I am developing a program that transforms artifacts in one (computer) language to artifacts in another language. In my program there are certain border line situations where the result of applyin the ...
1
vote
1answer
41 views

How can I name a $(a+x)\cdot b$ function

I'm looking for a name to identify functions like $f(x) = (x + a)\cdot b$. Does this kind of function have a specific name (like "affine" for $a\cdot x+b$)?
2
votes
1answer
79 views

Is there a common name for the property $f(\lambda x+(1-\lambda)y)\leq f(x)+f(y)$?

For $X$ a vector space and $f:X\to\mathbb{R}$, I'm considering the property $$f(\lambda x+(1-\lambda)y)\leq f(x)+f(y) \qquad\forall x,y\in X, \;\forall\lambda\in[0,1].$$ So it's like convexity ...
1
vote
2answers
234 views

What does it mean to be proportional to something?

I am asked a physics homework question, but it is really simply a mathematical question I think, dealing with proportional reasoning. The period of a pendulum is proportional to the square root of ...
1
vote
1answer
194 views

Undefined function

If we have an element of the set of real numbers i.e. '-3' and we have the square-root function i.e. $f(x) = \sqrt x$, then $f(-3) = \sqrt {-3}$ is undefined and the ordered pair $(-3, \sqrt {-3})$ is ...
1
vote
2answers
60 views

Is there a name for a relationship like idempotence between two functions?

If $f(f(x)) = f(x) \quad \forall \space x$ then $f$ is idempotent. If $g(f(x)) = f(x) \quad \forall \space x$ then is there a term to describe the relationship between $g$ and $f$?
2
votes
1answer
67 views

What is the opposite of a lift?

If I have a function $p:\tilde X\to X$ and a function $f:Y\to X$ , then a function $\tilde f:Y\to\tilde X$ such that $p\circ\tilde f=f$ is called a lift of $f$ with respect to $p$. So a lift is just a ...
2
votes
1answer
31 views

Every subset of A is f-saturated

Let $f:A\rightarrow B$ be a function such that $\forall X\subseteq A[ f^{-1}[f[X]]=X]$ (In other words, every subset of $A$ is $f$-saturated). Does the property of the function $f$ have a name ? I ...
3
votes
1answer
952 views

Difference between functional and function.

I have come across the term 'functional'. How is a 'functional' different from a 'function'? The exact term I came across was 'statistical functional.' In terms of the background, can you please ...
5
votes
2answers
155 views

Function notation terminology

Given the function $f:X\longrightarrow Y$, $X$ is called the domain while $Y$ is called the codomain. But what do you call $f(x)=x^2$ in this context, where $x\in X$? That is to say - what is the name ...
4
votes
0answers
115 views

Terminology Question: Precompose vs Compose?

I was wondering if there was a standard convention on what 'precompose' means compared to 'compose', as I am often confused between the two when all sorts of text casually use both terminologies. For ...
0
votes
1answer
91 views

Is there a generally accepted name for the function $f = \{0 \text{ when } x=0, 1 \text{ when } x ≠0 \}$?

In one of my computer programming projects I have defined the following quite common function: $$ f(x) = \begin{cases} 0, & \text{ when } x = 0, \\ 1, & \text{ when } x \neq 0. ...
2
votes
1answer
601 views

What is the difference between a function and a map? [duplicate]

Possible Duplicate: Is there any difference between mapping and function? I am an aspiring mathematician who just started out. What is the difference between a function and a map? Or are ...
3
votes
1answer
32 views

Symmetry and singularities

The function $f(x) = x$ is point symmetric. But what's with $g(x) = (x^2 - x)/(x - 1)$? $\mathbb{D}_g = \mathbb{R} \backslash \{1\}$ $g(x) = -g(-x)$ is true for every $x \in \mathbb{R} \backslash ...
2
votes
2answers
80 views

Is there such a thing as function decomposability?

I am not a mathematician, so what I ask might be trivial, however I couldn't find something relevant in the web. My question is the following: Is there a formal notation for functions that comply the ...
1
vote
1answer
285 views

Are “deterministic” and “idempotent” just two different names of the same concept? [closed]

Sometimes I encounter the term "deterministic" and sometimes I encounter "idempotent" in describing functions . Are they just ...
1
vote
0answers
43 views

Looking for correct terminology

Given the functions $f\colon A\to B$ and $g\colon B\to B$, a common, useful strategy is to define a new function $h\colon A\to A$ as the composition $f^{-1}\circ g\circ f$. There seem to be many ...
9
votes
2answers
607 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 ...
2
votes
2answers
129 views

Subset of a function

Suppose we have a function $f:X \rightarrow Y$. Now, consider the function $g:X'\rightarrow Y$ where $X'\subset X$. I'd like to say the $g$ is a "subset" of $f$ ; is there a correct term for ...