0
votes
0answers
17 views

Notation Question with regard to functions

Let $f : N → N$ Let $E(f)$ be the function defined by $E(f)(n) = 2^{f(n)}$. Does $E(f)(n)$ mean $E(f(n))$? or $E(f)(n)$?
2
votes
3answers
66 views

Use of $\mapsto$ and $\to$

I'm confused as to when one uses $\mapsto$ and when one uses $\to$. From what I understand, we use $\to$ when dealing with sets and $\mapsto$ when dealing with elements but I'm not entirely sure. ...
1
vote
3answers
68 views

Set notation and mappings question

Good evening. I have a question. Suppose I have two sets, $A=\{1,2,3,4\}$ and $B=\{5,6\}$. I want to write the notation for a function that takes each element in $A$ and assigns to it a value in $B$. ...
1
vote
2answers
43 views

Partial derivative in two dimensions

I am struggling with section 3.3 of the following thesis https://smartech.gatech.edu/xmlui/bitstream/handle/1853/29610/grigo_alexander_200908_phd.pdf. Page 21 is fine, then the problems occur in ...
0
votes
1answer
54 views

How to find the domains of functions $f(x) = x-5$, $g(x) = \sqrt{x-5}$, and of their sim?

I've been studying on Study Plan Practice, on MyMathLab for my College Algebra class. We're going over the Algebra of Functions right now and several things don't make much sense. The question is: ...
3
votes
2answers
61 views

In composition of two mappings, can the outer mapping access the arguments of the inner mapping?

In composition of two mappings, can the outer mapping access the arguments of the inner mapping? Here is an example to illustrate my question and my thought. E.g. $f: \cup_{n \in \mathbb N} \mathbb ...
1
vote
1answer
47 views

$f\in C(\mathbb{R})$. What does it mean?

$f\in C(\mathbb{R})$. What does it mean? My guess is "Differentiable on $\mathbb{R}$" but I'm not sure.. Thanks.
0
votes
1answer
80 views

Is $C(C(\mathbb R))$ notation for the set of continuous functions mapping $C(\mathbb R)$ to itself?

Given that in general functional analysis we have $C(\mathbb{R})$ being the set of all continuous functions, $f: \mathbb{R} \to \mathbb{R}$. However, could I use $C(C(\mathbb{R}))$ notationally to be ...
2
votes
0answers
41 views

notation for minimum and maximum?

I'm trying to figure out the correct notation for this situation for use in Machine Learning. I have various ratings (for texts): ...
6
votes
5answers
506 views

Functional Notation.

I have some doubts regarding function notation: First If I present a function I write:$f(x)$ If I write it's inverse:$f^{-1}(x)$ So why doesn't$f(f(x))=f^2(x)$ Second If $\frac{df(x)}{dx}=f'(x)$ ...
5
votes
2answers
78 views

What is this notation for a function? I've never seen it written like this before.

What does this mean? $$ f=\{ (x,y): y= x+2 \}$$ I don't understand what "$(x,y):$" means in regard to the problem. Also why is the $y$ inside of the $f(x)$ function. Isn't it supposed to be outside? ...
0
votes
0answers
67 views

What does $X:Y\to x(t)$ mean?

Relatively new into math and working my way into it. I need some help understanding the statement below. X:Y -> x(t). Can someone please help me with what does it mean? So just to clarify I have a ...
0
votes
0answers
43 views

Hyperbolic sinc function

Cardinal sine function or sinc function is defined by: \begin{equation} \mathrm{sinc}x=\begin{cases}\frac{\sin x}{x}, & x \neq 0,\\ 1, & x = 0,\end{cases} \end{equation} Is there any ...
0
votes
2answers
58 views

How to represent the ceiling function using mathematical notation?

How to represent the ceiling function using mathematical notation? I need an equation to input in a program because it doesn't except the ceiling function so it has to be some sort of mathematical ...
0
votes
2answers
43 views

Combinaision of two functions

Let us denote $X_0 = \{x, y\}$ and $X_1 = \{a, b\}$ two disjoint sets of variables; let us denote $V$ a set of values. I have two functions $f_0 : X_0 \rightarrow V$ and $f_1 : X_1 \rightarrow V$, ...
0
votes
0answers
24 views

Is there accepted notation and/or terminology for the smallest cover of $S$ with cells from $P$?

Let $X$ denote a set. Then for $S \subseteq X$ and $P$ a partitioning of $X$, define $P \diamond S$ as the smallest cover of $S$ with cells from $P$. Explicitly: $$P \diamond S = \bigcup\{Q \in P ...
0
votes
1answer
32 views

How to make clear a letter is a function?

How should I make clear that a symbol is a function? Usually a function is denoted by the letter $f$ or $g$, or is directly applied to arguments (e.g. $c(x,y)$) or is implied to be a function by an ...
0
votes
3answers
111 views

What is the $\lor$ symbol?

In researching the consensus algorithm, I came upon the consensus theorem: How does the $\lor$ symbol function?
0
votes
1answer
25 views

Express function counting number of elements in subsets

I wish to express a function $freq(x)$ as an equation but I have no clue how to properly do this. Basically I have the following: Let $a_i \subset A$ be one of many subsets of A. Each subset $a_i$ ...
1
vote
1answer
21 views

Definition of the Domain of a Function when the sets are the elements

In case I have a function that calculate the normalized distance of elements in two sets $A$ and $B$ I can define the function as $\mathrm{elementDistance} : A \times B \rightarrow [0,1]$. But if I ...
0
votes
1answer
35 views

Definition of Kronecker Delta

Is $\delta _{mn}=1$ when $m\neq n$, and $\delta _{mm}=0$? I am not very good at Math. So would you give me the answer and explanation please?
0
votes
1answer
21 views

Function with similar properties

Suppose I have a function $f$ and derive another function from it with similar properties. For example I have that my new function is zero when the other function is zero. I would still like to use ...
2
votes
1answer
27 views

Domain of a composite function

I was given the question: Find the domain of the function $f(x)=\ln(\ln(\ln x))$ I found the answer by inspection: $\qquad D(\ln x)=(0,\infty)$ $\therefore\quad D(\ln(\ln x))=(1,\infty)$ ...
3
votes
1answer
38 views

Is there standard notation to handle “chains of functions”?

Let $f(x)=g $ $g(y)=z $ Is there standard notation to express z in terms of f(x)? Something like (f(x))(y)?
1
vote
2answers
41 views

Iterated self-composition of arbitrary function

Does there exist some notation that represents the iterative composition of a single-input, single-output function with itself? As in, say, $f_5(x)=f(f(f(f(f(x)))))$. In other words, going by the ...
0
votes
1answer
43 views

Notation regarding the maximum function over a list of naturals

So I'm trying to write down the maximum function(with a precise mathematical notation) over a set of integers by utilizing the generic maximum function which takes two integers, $max: \mathbb{N} ...
0
votes
1answer
24 views

Expression as argument in function definition

When a function definition has an expression (instead of just a single variable) as the argument to the function, what does this mean? For example, I have this question (part b): Given a certain ...
4
votes
1answer
83 views

Is there a difference between writing $f: X\rightarrow Y$ and writing $f:X\mapsto Y$?

I think I've heard about a year ago that "$\mapsto$" is only used for a bijection, or do they mean the same thing?
1
vote
0answers
26 views

Groups - Compositions

If the f is written to the right of its argument does that mean the composition of $f g$ is actually $g(f(x))$ instead of being $f(g(x))$ which is the notation I'm used to. I ask this because I read ...
0
votes
1answer
41 views

Notation for partial function set.

There is a standard notation for the set of all functions between S and T, namely T^S. Is there a similar notation for the set of all partial functions between S and T?
-1
votes
1answer
39 views

What is the place holder glyph for a set?

What glyph do set theorists use to denote an unspecified set? For example, logicians use φ to talk about an unspecified sentence in first order logic. Does set theory have a comparable glyph? Thank ...
2
votes
0answers
19 views

Large Composition Operator?

Doing composition of functions with my students and was wondering if there was a large composition operator similar to Sigma and Pi? What I'm thinking is composing a function n times... $$(f\circ ...
1
vote
1answer
18 views

'Union' of maps

Let $f : A \to Y$, $g : B \to Y$. Suppose that $f(x) = g(x)$ whenever $x \in A \cap B$. Define $$ h : A \cup B \to Y, \\ h(x) = \begin{cases} f(x) & \text{ if $x \in A$} \\ g(x) & \text{ if ...
0
votes
2answers
50 views

function application order

In traditional mathematics, when we post-compose $x$ by $f$ we write $fx$ or $f(x)$, that is we prefix writing things right to left. I realize some might be used to it, and it is absolutely trivial, ...
0
votes
0answers
97 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 ...
1
vote
1answer
59 views

Subscript before a function symbol?

Does anyone know what the subscript before the function means? $$ _pf_p $$ It's part of a definition for selfish routing in networks: Let $N = (V,E)$ be the network, which is a directed graph. ...
2
votes
0answers
37 views

How should I interpret this function notation?

I'm trying to implement an FDGD Algorithm from a paper and I'm a little stuck how to interpret a piece of function notation. See page 7, equations 2 and 3 in this document: In there we have ...
0
votes
0answers
22 views

Expressing three recursive forms into one using parameters?

I have the following recursive function that takes three forms and I want to express it in one form: Initial: $f(x) = m * f(x-1)$, $f(0) = value.$ Forms: 1 - $f(t) = m * f(t-1)$. where t is at ...
0
votes
3answers
75 views

Function Notation question that needs an answer

$f(x)= f(x+1)+3$ and $f(2)= 5$, determine the value of $f(8)$. I don't understand how $f(x)$ can equal $f(x+1)+3$
8
votes
3answers
195 views

Regarding the notation $f: a \mapsto b$

While I have come to understand that $f:a\mapsto b$ means that for input from the set $a$, the function will return a value from the set $b$, I am curious as to how far one may "drag" this notation. ...
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 ...
0
votes
3answers
76 views

Express the range of a Domain Subset [Notation]

I got a Function f with Domain A and Range B, if S is a subset of A, how can I express the set of the computed values of s with function f?.
1
vote
1answer
39 views

On notation for derivative of an n-Dimensional Gaussian

How to we represent the derivative of a n-D gaussian function defined by $g(\mathbf{x}) = \dfrac{1}{\sqrt{2 \pi \left|\Sigma\right|} } \exp^{-\dfrac{1}{2}({\mathbf{x}-\boldsymbol\mu}) ^\top \Sigma ...
2
votes
1answer
75 views

$f(x) \neq x$ ambiguity?

The question is : An integer function $f(x)$ is valid only for $x = 0, 1, 2, 3$ and has an interesting property $f(f(x)) = x$. It is also known that $f(x) \ne x$. Find out how many such functions ...
1
vote
1answer
63 views

Can subscripts be used like this?

I have a variable named $P$, and another three variables named $P_c$, $P_d$ and $P_u$. Now, if I define this function: $$f(x) = x_c + x_d + x_u$$ Is it correct to say that: $$f(P) = P_c + P_d + P_u$$ ...
1
vote
1answer
79 views

Definition of functions on metric spaces.

In the post Definition of functions, it is stated in the accepted answer that one way to define a function is to define it as the triple $(f, X, Y)$ where $f \subset X \times Y$. My question is what ...
-1
votes
2answers
34 views

Applying a function to a set rather than a value

I do apologize about the title, I dont understand the question so I couldnt come up with a better title, if someone else could edit it to a more meaningful title I would appreciate it. So here is the ...
0
votes
1answer
28 views

Notation to describe amount of relevant elements in a tuple?

Say, we have the set $A=\{♠,♣,♥,♦\}^3$ and would like to define the following map: \begin{align} f: A &\to \{0,1,2,3\} \\ a &\mapsto \text{amount of ♥'s in the tuple } a \end{align} For ...
1
vote
2answers
89 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
2answers
137 views

Notation of a function that maps a random element

Let there be a functions $f$ and $g$ such that, $$f:A \times B \mapsto \Re$$ $$g: B \mapsto A$$ where $\forall b \in B$, $g(b)$ is some $a$ such that, $\forall a' \in A, f(a,b) \geq f(a',b)$. (This ...