0
votes
0answers
22 views

correct use of notation in defining a function

So I have this function which takes a integer tuple and another tuple, and maps them to a value from some pre-defined set of values. I had the following signature: $\omega:(\mathbb{N} \times ...
0
votes
1answer
12 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
64 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
21 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
25 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
14 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
47 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
54 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
54 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
29 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
21 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
61 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
4answers
137 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
140 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
55 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
33 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
71 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
58 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
66 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
32 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
26 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
79 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
74 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
31 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
25 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
25 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
80 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
104 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
0answers
190 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
94 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
108 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
41 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
64 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 ...
2
votes
3answers
114 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
137 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
1
vote
1answer
24 views

How would you explicitly define the number type of a function's parameters?

Say I make a function $f$ that takes a parameter $a$, but I want to make sure that $a$ can only be $\mathbb{N}$, no $\mathbb{Z}$ or $\mathbb{R}$ allowed (as an example), how would I write that in a ...
0
votes
1answer
100 views

Which way of writing functions is the most correct?

In functional programming it's not uncommon to bind a closure/lambda/anonymous function to a value name, i.e. $$f = x \mapsto x^2 + 3$$ so I've been wondering which is more right to do in ...
2
votes
3answers
170 views

What does $f: A \times A \to A$ mean?

What does $f: A \times A \to A$ mean? Can you give some examples please?
2
votes
0answers
40 views

Notation for n-array function with domains of different types.

I'm wondering what notation I should use to express a function R that maps elements from different sets to either 0 or 1. Is the following a reasonable usage? $$ R: S_1 \times S_2 \times ... \times ...
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 ...
1
vote
4answers
183 views

What is rigorous notation for functions?

I have seen many ways to denote a function: $f(x)=x^2, y=x^2, f: x\mapsto x^2$ and so on. What is exact notation for functions? Please include lethal doses of rigor, set theory, and of course ...
17
votes
12answers
3k views

How to represent the floor function using mathematical notation?

I'm curious as to how the floor function can be defined using mathematical notation. What I mean by this, is, instead of a word-based explanation (i.e. "The closest integer that is not greater than ...
2
votes
6answers
207 views

Function Notation

due to our national cirriculum (the way in which it was taught in high school). We just said that f(x) means a function. Though I understand this isn't necessarily correct? In high school we used ...
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 ...