# Tagged Questions

42 views

### Combinaision of two functions

Let us denote $X_0 = \{x, y\}$ and $X_1 = \{a, b\}$ two disjoint sets of variables; let us denote $V$ a set of values. I have two functions $f_0 : X_0 \rightarrow V$ and $f_1 : X_1 \rightarrow V$, ...
36 views

### problems on define set with polynomials

I'm trying to say set A is the set of nonnegative integers that not of this two forms $3x^2 + (6y-4)x - y\$ and $\ 3x^2 + (6y-2)x + (y - 1)$, for example: $4=3 \cdot1^2+(6 \cdot1-4) \cdot 1-1\$ is ...
92 views

### Which is the best notation for a sequence?

In a set, the order of its elements is (as far as I know) not important; in a sequence, the order of its elements is important. Which is the notation I should use in order to define a sequence? I ...
135 views

### Usage of $\cdot$ in calculus

I often find myself caught in the dilemma of whether or not to use the symbol $\cdot$ in calculus. Take for example, the chain rule: $$\frac{dy}{dx} = \frac{dy}{du}\cdot\frac{du}{dx}$$ Is the ...
47 views

### Name and notation convention for “unnormalized probability”

Given a finite set of non-negative numbers $S={s_1,...,s_n}$, we can divide them by a normalization constant $Z$ (i.e. their sum) to get a probability distribution. Then we typically say (and write) ...
45 views

### Semidirect product notation convention

I was taught that if $G \simeq H \ltimes K$, then (by convention) $H$ is the subgroup that is normal, but I see on Wikipedia and elsewhere that other people use the convention that the above indicates ...
522 views

### What are reasons why some symbols in mathematical logic are not standardized?

Why is so hard to find a standardisation regarding symbolism and/or terminology in Mathematical Logic ? We see again and again students asking if e.g. $\rightarrow$ and $\implies$ means the same ...
48 views

### Notation in functions spaces

I'm wondering if there is a convention for the following. Let $g:\mathbb{R}^2\to \mathbb{R}$ be given and u in $C^1(\mathbb{R})$. I'm looking for a notation for $g(x,u(x))$ is in the space of ...
109 views

### Category of topological pairs

Is there a standard abbreviation for the category of topological pairs? I have searched for it in vain.
85 views

### Why is $m$ used as the variable for slope in slope-intercept form?

I was wondering if you could answer a question I have on slope intercept form of a linear equation. I know its $y=mx+b$, but why is it $mx+b$? Don't get me wrong. I know that $m$ is the slope and $b$ ...
33 views

### Value expressions

What is the value of the expression: $\sum_{k=0}^{d}b^{k}\left[\begin{array}{c} d\\ k \end{array}\right]\prod_{i=0}^{k-1}\left(c-b^{i}\right)$ for $k = 0$? In particular, what is then the value ...
174 views

202 views

### Convention of writing constraint sets

As I will write constraint sets very often, I would like to make sure that I respect the convention. First, I would like to represent a set of constraints and their relation are conjunction. For ...
54 views

### Are segments and intervals always subsets of $\mathbb{R}$?

Which of the following is the accepted mathematical practice? Any segment $(a, b)$ or interval $[a, b]$ contains only real numbers. If you want all the rational numbers between $a$ and $b$, you ...
183 views

### Good Hygiene in using Quantifiers

When using quantifiers it is probably important to pick up certain habits that Veterans agree upon as early as possible. Since it was pointed out to me by a highly esteemed member that it's ...
959 views

### use of $\sum$ for uncountable indexing set

I was wondering whether it makes sense to use the $\sum$ notation for uncountable indexing sets. For example it seems to me it would not make sense to say  \sum_{a \in A} a \quad \text{where A is ...