# Tagged Questions

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### Calculate random integer inside a range of real numbers

$$F : \Bbb R \times \Bbb R \rightarrow \Bbb N$$ $$F(\text{minReal},\ \text{maxReal}) = \text{randomInt} \in \left[\text{minReal},\ \text{maxReal}\right]$$ Let $r \in [0, 1)$ be a random value. How ...
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### Why do we define functions to be set theoretic objects?

Why do we define functions to be set theoretic objects? Functions are so intuitive, why do we define it in complicated set theory language?
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### What is real periodic function

I would like to know what is real periodic function. I understand what is periodic function, but I do not understand what is "real" periodic function.
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### Alternative to epsilon-delta definition

Back in Multivariable Calculus, I remember my professor, when explaining why he decided to skip a rigorous definition of limit (the reason was that those of us that would continue in math would go ...
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### Definition of standard functions [duplicate]

In many texts and books about calculus we see There are functions $f$ for which the anti-derivative cannot be expressed in terms of standard functions or there are many integrals that cannot ...
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### Motivation for defining a functions codomain

Why not always refer to a functions image, what is the point in specifying some super set of that image and then naming that super set the functions "codomain"? What does explicitly defining a set ...
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### Codomain of a function

At high school we were told that a function has a domain and a range, the function maps from the domain to the range. Such that the domain contains all and only the possible inputs and the range ...
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### Precise definition of oscillation behavior of functions like $\sin(\frac1{x})$

I tried today precisely defining the oscillation behavior present in functions like $\sin(\frac1{x})$ i.e: To do this, I started with the domain of function as in limits, and let $f(x)-L$ have ...
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### Beginning Proof on functions and Sum of functions

I've been having a hard time with this proof because I do not know where to go from where I am. The proof we were assigned to in class is as follows: Let $f : \mathbb Z \rightarrow \mathbb Z$ be a ...
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### What are some practical uses of functions? [closed]

Functions are basically formal equations that relate a set of inputs to output. What are some practical uses for functions and inverse functions?
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### Notation for Partial Functions

Suppose we have sets $f$, $A$ and $B$ such that $f\subset A\times B$ and $\forall x\in A\space \forall y,z\in B: [(x,y)\in f \land (x,z)\in f \implies y=z]$ i.e. $f$ is a partial function mapping ...
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### Odd and even functions.

I have a book which says: If a function $f$ satisfies $f(-x)=f(x)$ for all $x$ in its domain, then $f$ is called an even function. However, if $f(-x)=-f(x)$ for every $x$ in the domain of $f$, ...
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### Linear function definition

I'm trying to figure out what is linearity and what is a linear function. But the wikipedia page confused me. Firstly it defines as polynomial : $f(x) = ax +c$ Than it defines as linear map: ...
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### What is the proper term for a function where domain and codomain coincide?

What is the proper term for a function where domain and codomain coincide? E.g. in programming languages a function f : Int => Int or f : Double => Double. Thanks.
From wikipedia I obtain the following definition of an injective function : Let $f$ be a function whose domain is a set $A$. The function $f$ is injective if for all $a$ and $b$ in $A$, if \$f(a) = ...