# Questions tagged [terminology]

Questions on the usage and meaning of words in mathematics, the names for mathematical entities, and other such questions.

5,595 questions
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### Name for a coordinate system defined on a [unit] sphere

One of the commonly used coordinate systems in 3D is a spherical one. Which would be defined by: a radius $r$ polar and azimuthal angles $\theta$ and $\phi$, where "mathematicians and physicists ...
2answers
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### What is the difference between a definition and an equivalence class?

In what way is 'the definition of $x$ is $y$' ($x:=y$) not the same as '$x$ is equivalent to $y$' ($x=y$)? I can find no justification for making the distinction aside from 'it feels right'. It seems ...
2answers
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### “Dimension of a vector” vs. “Directions of a vector”

A vector like $(7,5,4)$ is said to have the dimension of 3. But I have also heard that the "5" is the "second dimension of the vector". In the later case one would say the vector has three dimensions (...
3answers
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### X is to vector like matrix is to linear operator?

In linear algebra texts there is usually a clear distinction between linear operators and matrices. A linear operator is a map between two spaces that fulfills a set of conditions. A matrix is a 2D ...
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### What do you call a “factor” of a union

If we have numbers $a,b$, they are called summands of $a+b$ or factors of $a\cdot b$. Given two modules $M,N$, they are direct summands of $M\oplus N$. Likewise, given two sets $A,B$, they can be ...
1answer
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### Subgroup of finitely-generated subgroup

Is there a standard name for this concept: Let $H \leq G$ be groups. Say $H$ is ?? if there is a finitely-generated group $K \leq G$ such that $H \leq K$. What should one use in place of "??"? I'm ...
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### What was the motivation behind the fraction ideal's name?

The fraction ideal is the ideal $$(I:J)=\{x\in R:xJ\subseteq I\}$$where $I, J$ are ideals in $R$. My question is, why is it called a fraction ideal? (Sometimes it is called the "Ideal quotient of $I$ ...
1answer
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### Map Vs. Mapping?

I am so confused in the usage of the words: Map and Mapping. For example, consider the mapping: $T:W^{2,p}(\Omega)\rightarrow L^{p}(\Omega)$ defined by $T(u):=\Delta u.$ Can we write: consider the ...
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