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### 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 ...
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1k 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?
2k 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 ...
414 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 ...
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188 views

### Mapping vs function [duplicate]

I am reading an engineering mathematics book whose author says that the term mapping and function have the same meaning and whether one calls $f:X\rightarrow Z$ a function or mapping is a matter of ...
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### 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 ..."
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### 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 ...
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### 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
4k 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\\ \...
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### 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 ...
637 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 ...
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### 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 $G\rightarrow{G}$ ...
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### Maps between topological spaces; any rules?

So I understand that for a "continuous" map between topological spaces, the pre-image of an open subset is an open subset. (There is no 'inverse map' unless the function is bijective, so careful there)...
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### 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 ...
1 vote