# Tagged Questions

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### 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): ...
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### 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 $\frac{df(x)}{dx}=f'(x)$ ...
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### 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? ...
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### 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 ...
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### Hyperbolic sinc function

Cardinal sine function or sinc function is defined by: $$\mathrm{sinc}x=\begin{cases}\frac{\sin x}{x}, & x \neq 0,\\ 1, & x = 0,\end{cases}$$ Is there any ...
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### 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 ...
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### 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 $f_1 : X_1 \rightarrow V$, ...
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Let $f : A \to Y$, $g : B \to Y$. Suppose that $f(x) = g(x)$ whenever $x \in A \cap B$. Define $$h : A \cup B \to Y, \\ h(x) = \begin{cases} f(x) & \text{ if x \in A} \\ g(x) & \text{ if ... 2answers 50 views ### function application order In traditional mathematics, when we post-compose x by f we write fx or f(x), that is we prefix writing things right to left. I realize some might be used to it, and it is absolutely trivial, ... 0answers 87 views ### About Kernel and the coimage of a function Introduction I was serching for a concept of "equivalence relations" induced by an arbitrary function in a "natural" way and I found the concept of Kernel. But I'm not sure that I understand it and ... 1answer 57 views ### Subscript before a function symbol? Does anyone know what the subscript before the function means?$$ _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. ... 0answers 34 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 ... 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 ... 3answers 74 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 3answers 182 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. ... 4answers 172 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 ... 3answers 70 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?. 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 ... 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 ... 1answer 62 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... 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 ... 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 ... 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 ... 2answers 87 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 ... 2answers 129 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 \Reg: B \mapsto A$$where \forall b \in B, g(b) is some a such that, \forall a' \in A, f(a,b) \geq f(a',b). (This ... 2answers 36 views ### notation question re: function space This is a quick notation question: when one writes X: C[0,\infty) \to \mathbb{R}, what does that mean exactly? Is C[0,\infty) the space of continuous functions with a domain of [0,\infty) and ... 1answer 26 views ### Validity of notation from the aspect of function description I have the following notation that should describe the nature of my function for \forall a \in A \exists f:A \rightarrow S, A \subset N, S \subset [0,1]^n,|S|=n Can anyone tell me is the notation ... 1answer 60 views ### Is g(x,y) = f(\frac{x}{2},\frac{y}{2}) correct notation? I was a bit confused when I saw this statement g(x,y) = 2f(\frac{x}{2},\frac{y}{2}), and seeing it used in a double integral \int \int g(x,y) = 2 \int \int f(\frac{x}{2},\frac{x}{2}) \, dx dy. I ... 0answers 26 views ### “Anti-cumulative” Relation Image using Intersection Given a binary relation R \subseteq X \times Y, the familiar image of some A \subseteq X is defined as R[A] = \{y\ |\ (x, y) \in R, x \in A\}. Naturally we have the property R[A] = \bigcup_{x ... 0answers 24 views ### Restricting binary relations by composing with an “inclusion binary relation” If X' \subseteq X then we may define an inclusion map \iota : X' \to X where \iota(x) = x. One use of \iota is that we can express the restriction of some f : X \to Y to X' as f|_{X'} = f ... 1answer 82 views ### Wrong use of function notation f(n) I've recently read in a book about computational complexity theory:$$ 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 ...
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 ...
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 ...