# Tagged Questions

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### How to check the availability of particular function [on hold]

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...
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### What is the $\lor$ symbol?

In researching the consensus algorithm, I came upon the consensus theorem: How does the $\lor$ symbol function?
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### 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 $a_i$ ...
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### 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 ...
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### 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 ...
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### 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: $\qquad D(\ln x)=(0,\infty)$ $\therefore\quad D(\ln(\ln x))=(1,\infty)$ ...
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### 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)?
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### 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 ...
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### $f(x) \neq x$ 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 ...
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### 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: $$f(P) = P_c + P_d + P_u$$ ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
What does this symbol mean? Please i need help: Its the symbol just before "$H^{t-1}$". Thanks for help
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 ...