0
votes
1answer
27 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 ...
-7
votes
0answers
21 views

How to check the availability of particular function [closed]

I want to check the availability of particular function that returns the value of results in binary like 0 or 1....How to check these function using mathematics...
0
votes
3answers
106 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
21 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
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
20 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
37 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
33 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
21 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
76 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
0answers
30 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
16 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
17 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
80 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
57 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
32 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
71 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 $f(x+1)+3$
7
votes
3answers
166 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
166 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
68 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
38 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
61 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
77 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 ...
0
votes
2answers
33 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
86 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
119 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 ...
0
votes
2answers
36 views

notation question re: function space

This is a quick notation question: when one writes $X: C[0,\infty) \to \mathbb{R}$, what does that mean exactly? Is $C[0,\infty)$ the space of continuous functions with a domain of $[0,\infty)$ and ...
0
votes
1answer
26 views

Validity of notation from the aspect of function description

I have the following notation that should describe the nature of my function $for \forall a \in A \exists f:A \rightarrow S, A \subset N, S \subset [0,1]^n,|S|=n$ Can anyone tell me is the notation ...
1
vote
1answer
54 views

Is $g(x,y) = f(\frac{x}{2},\frac{y}{2})$ correct notation?

I was a bit confused when I saw this statement $g(x,y) = 2f(\frac{x}{2},\frac{y}{2})$, and seeing it used in a double integral $\int \int g(x,y) = 2 \int \int f(\frac{x}{2},\frac{x}{2}) \, dx dy$. I ...
0
votes
0answers
26 views

“Anti-cumulative” Relation Image using Intersection

Given a binary relation $R \subseteq X \times Y$, the familiar image of some $A \subseteq X$ is defined as $R[A] = \{y\ |\ (x, y) \in R, x \in A\}$. Naturally we have the property $R[A] = \bigcup_{x ...
0
votes
0answers
23 views

Restricting binary relations by composing with an “inclusion binary relation”

If $X' \subseteq X$ then we may define an inclusion map $\iota : X' \to X$ where $\iota(x) = x$. One use of $\iota$ is that we can express the restriction of some $f : X \to Y$ to $X'$ as $f|_{X'} = f ...
6
votes
1answer
81 views

Wrong use of function notation $f(n)$

I've recently read in a book about computational complexity theory: $$ O(f(n)) = \{g:\mathbb N \to\mathbb R \cup \{0\} : \exists \xi > 0,n_0\in \mathbb N\;\: g(n) \leq \xi \cdot f(n) \;\: \forall n ...
0
votes
1answer
33 views

Issues with notation

I have this definition, and I am having difficulties with notation: Maybe I should explain a little bit: $D_{1}$ and $D_{2}$ are two matrices (or databases) with the same number of columns, but ...
0
votes
1answer
114 views

Function and dependent variable are represented by the same symbol?

Is it wrong to represent a dependent variable and a function using the same symbol? For example, can we write the parametric equations of a curve in xy-plane as $x=x(t)$ , $y=y(t)$ where $t$ is the ...
1
vote
1answer
230 views

using the same symbol for dependent variable and function?

Is it wrong to represent a dependent variable and a function using the same symbol? For example, can we write the parametric equations of a curve in xy-plane as $x=x(t)$, $y=y(t)$ where $t$ is the ...
1
vote
2answers
99 views

Preimage of a function

The only way to get better at this sort of thing is to practice, and now I'm also trying to ask myself (and try to answer) more conceptual questions. If a circle with radius $r$ is given in ...
0
votes
0answers
150 views

Notation for domain-restricted function

When restricting the domain of a function $f: A \to B$ it is common to write $f|_{E}$, to mean $f$ domain-restricted to $E \subseteq A$. This notation is used in Wikipedia and also for example in this ...
1
vote
2answers
51 views

Power correct notation

Ok, I know this may sound dumb, but I am trying to understand which is the correct (most beauty) notation for the power function ${\rm pow}(f(x),n)$. This is the correct one: $[f(x)]^n$ From ...
0
votes
2answers
68 views

About notation of function

Suppose I have a function $f:[a,b] \to \mathbb{R}$. I am writing this: $f$ is a nice function. Is this sentence the same as the sentence $t \mapsto f(t)$ is a nice function. In other ...
3
votes
3answers
147 views

Different of mapsto and right arrow

Could someone please explain to me what is the difference in the two arrows$$\rightarrow$$ and $$\mapsto$$ For example in Probability wih Martingales (Willams) Thank you.
2
votes
2answers
158 views

What does it mean when a function $f$ has a subscript that is an indexing set $A$? That is, $f_A$.

I'm reading Intro to Topology by Mendelson. I'm having trouble understanding certain notation he uses for a particular problem. To put it into context, here is the problem at hand Let ...
3
votes
0answers
92 views

What “double bracket” means? [duplicate]

What does this symbol mean? Please i need help: Its the symbol just before "$H^{t-1}$". Thanks for help