Linked Questions

5
votes
1answer
5k views

What is the difference between a function and a map? [duplicate]

Possible Duplicate: Is there any difference between mapping and function? I am an aspiring mathematician who just started out. What is the difference between a function and a map? Or are these ...
3
votes
2answers
456 views

what is the basic difference between a mapping and a function? [duplicate]

what is the basic difference between a mapping and a function? many say they are same but the opposite views are also seen. is mapping a restricted version of a function?
2
votes
2answers
1k views

What is the difference between linear mappings and linear functions? [duplicate]

Let $V$ and $V'$ be vector spaces over a field $K$. A linear mapping $$f:V \to V'$$ is a mapping which preserves addition and scalar multiplication. My question is: what is the difference between ...
0
votes
2answers
282 views

On mapping notation [duplicate]

So I’m in the midst of coming to grips with mapping notation and just require some clarity. Is there anything wrong with writing $$x\mapsto\frac{1}{x}$$ Because from my understanding, I understand ...
5
votes
0answers
132 views

Are the words “function”, “map”, and “mapping” synonymous? [duplicate]

Is it correct to say that "A function or a map or a mapping is a binary relation such that ..."
0
votes
1answer
43 views

Function, Mapping and Relation [duplicate]

I believe I understand what a function and relation are, but what is a mapping? At first I thought the term was synonyms with relation, but after looking it up, I’m thinking it could be more or less ...
6
votes
2answers
2k views

Orbit , trajectory, dynamical system

The orbit of $φ$ through $x_0$ is the set $O(x_0) \equiv \{φ_t(x_0) : −∞ < t < ∞\}$. This is also called the trajectory through $x_0$. Then, what is the difference between an orbit and a ...
1
vote
2answers
2k views

Piecewise functions “overlap”

The question asks "Decide whether the following is a function or not; justify your answer." Then they give the following piecewise "function": $$ f(x) = \begin{cases} x+1, & \text{if } x < 0\\ \...
2
votes
1answer
981 views

Necessity of being well-defined in Group Homomorphism?

In Group Theory, homomorphism is isomorphism when we no longer restrict to bijective map; do we still need that map to be well defined in homomorphism (like in isomorphism) or homomorphism can be ...
0
votes
2answers
675 views

What Exactly Is The General Concept Of A Mathematical “Mapping”? How Are The Mappings Used?

I am seeking to understand the concept of a "mapping" in Mathematics. I tried reading "pure" mathematical information, and I encountered the term "mapping." My interpretation of the term is that it ...
0
votes
2answers
111 views

What's the point of functions? [closed]

I do not understand why functions are needed in mathematics(algebra, to be exact). They are nearly the same as regular equations. Yeah, "there should be only one output for a particular input", and so ...
0
votes
2answers
80 views

Notational difference, functions and mappings, talking about sets and classes

A Function is a set of pairs such that no two pairs have the same first member. My question summarized: What if I want to consider proper classes of pairs? The closest question to mine I could find ...
1
vote
0answers
53 views

If $g\in{G}$ and G is a group, then the map $G\rightarrow{G}$ given by $x\mapsto{gx}$ is a bijection.

Right now, I am reading Evan Chen's Napkin to study Abstract Algebra and other various topics. In lemma 1.2.5, he states: Let $G$ be a group, and pick a $g\in{G}$. Then the map $G\rightarrow{G}$ ...
0
votes
0answers
26 views

How is this called?

In french, there is a word for what's called an "application" that can be bijective, injective or surjective, in english I only see the word "function". In french, an application is defined as a ...