# Questions tagged [terminology]

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

6,975 questions
Filter by
Sorted by
Tagged with
7 views

64k views

### Why does an infinite limit not exist?

I read in Stewart "single variable calculus" page 83 that the limit $$\lim_{x\to 0}{1/x^2}$$ does not exist. How precise is this statement knowing that this limit is $\infty$?. I thought saying the ...
36 views

### What is the term for simple (non-matrix) math?

Is there a term for "simple" arithmetic where all variables in the expression contain only single/scalar values and thus produce a scalar result? This is opposed to matrix math where a ...
72 views

### Why are some functions called 'forms'?

The question is simple: why are some functions called 'forms'? Modular 'forms', bilinear 'forms', differential 'forms', quadratic 'forms', and so forth. It is not concretely a mathematical question ...
15 views

### Term for repeated exponentiation?

Is there a term (or operation) for repeated exponentiation? I.e. Repeated addition is multiplication, repeated multiplication is exponentiation, repeated exponentiation is X? Is there even such a term ...
35 views

### Name of a certain set of vectors

Let $v,u\in V$, a normed vector space (or I guess a normed magma if we want to be general), and let $l=(l_1,\dots,l_n)$ be a list of positive lengths. Then what do you call the set of "chains&...
51 views

### Is there a name for function $f(x)=\max(a, \min(x, b))$, where $a \leq b$?

Is there a name for function $f(x)=\max(a, \min(x, b))$, where $a \leq b$? What actually this function does: it keeps value in bounds of $[a, b]$.
52 views

### Representation theory: terminology

I am learning about representation theory. One of the things which continually trips me up is the (abuse of?) notation $V$ for a representation. Normally, one writes $(\rho, V)$ for a representation, ...
25 views

### Property of $f(x, y)= z$ for all permutations of $x, y, z$

What property would you say a function $f(x, y)= z$ has if it is true for all permutations of values $x, y, z$?
52 views

### Is the length of a line a property of that line, or is it its own mathematical object?

I'm trying to understand the nature of mathematical objects. As far as I understand it, mathematics studies these objects. Geometric shapes are one kind of such object, including 1D shapes, namely ...
89 views

### Confusions with Symbol “=” in Mathematics

I am having this question because of the axiom of equality: \forall x \forall y \left(x = y \longrightarrow \forall z\left(z \in x \longleftrightarrow z \in y\right)\right). \end{...
61 views

### Ideal of a group

The ideal is defined in the ring theory; In ring theory, a branch of abstract algebra, an ideal of a ring is a special subset of its elements In the answer to this question What is the exponent of a ...
44 views

### Does a mathematical definition have necessary and sufficient condition hidden in it? [duplicate]

Let us assume the following definition:  S is said to be A if S satisfies the condition C. '' -----------(P) Can it mean that:  S is A if and only if S satisfies the condition C. '' ---------- (...
2k views

### Probability distribution vs. probability mass function (PMF): what is the difference between the terms?

Consider a discrete case. PMF is the probability each value of random variable gets. So, for example, X ~ Poisson(2). I plot these probabilities (below), so I can say that I show the PMF of X. But on ...
41 views

### Confusion on the definition of an indexed family of sets

Ive recently been learning set theory and a bit of topology and im very confused on the definition of an indexed family. Why do we say a family of sets instead of a collection of sets? And why is the ...
17 views

76 views

### Understanding Slope Better

Recently, I have realized how much I have taken for granted in understanding the slope of a line and the slope of a curve in general. With that said, I wanted to clear up my understanding to make sure ...