All Questions
Tagged with notation terminology
527
questions
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2
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128
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What is the definition of a differential equation's general solution?
I'm not an English speaker.
Sorry for my bad English.
What is the definition of a differential equation's general solution?
Definitions I've heard are
"a solution containing arbitrary ...
- 13
1
vote
1
answer
39
views
What mathematical terminology and equations are used for variant assertions of finite sets?
Below there is a set of variants (or enumerations) of multiple finite sets with a different number of items in each set.
I don't want to use the word combinations because I believe those are of the ...
- 462
1
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1
answer
94
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Are there terminologies for "one-to-one" but not "onto" functions, and "onto" but not "one-to-one" functions?
One-to-one (injective) functions are not necessarily not onto (not surjective).
Similarly, onto functions are not necessarily not one-to-one.
So, a function can be one-to-one and onto (bijective).
$f(...
- 5,450
0
votes
1
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65
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What is the term for when the power is written behind the base?
Some time ago I watched a video discussing the notation of a “backwards” exponent, where the power comes before the base (e.g. ³2). I was wondering:
a. What this term was called
b. How it works
Thanks
- 3
1
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1
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47
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Why is a resolution of portrait mode 480 x 640 described as 4 : 3 instead of 3 : 4?
As I've read that:
The aspect ratio of an image is the ratio of its width to its height.
For instance, if a rectangle has an aspect ratio of 2:1, then it is twice ...
- 113
1
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0
answers
28
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Is there a specific terminology for these upper unitriangular matrices?
I came across upper unitriangular $n \times n$ matrices of the following form (here for $n = 5$):
$$
\pmatrix{
1 & a & a^2 & a^3 & a^4 \\
0 & 1 & a & a^2 & a^3 \\
0 &...
- 40.7k
1
vote
1
answer
66
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Referencing a statement with quantifiers in two separate lines
I want to show that a statement with several quantifiers, e.g., "$f(a, b) <= 0$ for all $a\in [0, 3]$ and all $b\in [-\infty, -1]$", is equivalent to another statement with several ...
- 13
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0
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49
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What is the conventional name/notation for the function $ N(n) = \begin{cases} 1 & n \le 0 \\ n & n > 0 \end{cases}$?
I am wonder what the conventional name/notation for this function:
$$ N(n) = \begin{cases} 1 & n \le 0 \\ n & n > 0 \end{cases}$$
I assume its use is frequent enough that there is such a ...
- 1,129
0
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0
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11
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Terminology/notation for pulling back multi-sigma functions
I deal with a lot of multi-sigma functions, which I assign compact formulas through a step-wise "pull-back". It is best explained through a well-known example:
$$\begin{align} \sum_{i_1=1}^n ...
- 1,129
1
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42
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Terminology for set-valued functions that are "included" in another function
I was wondering, if you have $f:A \rightarrow B$ a mapping onto sets, is there appropriate terminology for when, for a subset $C \subseteq A$, you have $g:C \rightarrow D$ that verifies $\forall e \in ...
- 121
0
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13
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Term and notation for the maximal exponent that gives a power of a number that divides some other number [duplicate]
Consider two integer numbers $a$ and $b$, and let $n$ be the maximal natural number (or $0$) such that $a^n$ still divides $b$. Is there some standard term and/or notation for this $n$ (as a function ...
- 2,210
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33
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Axes of an ellipsoid
A 3-Dimensional ellipsoid is given by the equation:
$$\frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} = 1$$
Let $a=20, b=15$ and $c=10$. Then as per my understanding, $a$ is the major axes and $c$ ...
- 101
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69
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How to formally define this square matrix?
I was wondering if there is formal name for a 3x3 matrix where the third column is the sum of the first two columns and the third row is the sum of the first two rows. In other words, a square matrix ...
- 47
2
votes
1
answer
57
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Term for injective/one-to-one with respect to just one of multiple variables?
As I understand it , a function $z=f(x,y)$ would be one-to-one or injective if there is only one unique $(x_1,y_1)$ pair which yields some value $f(x_1,y_1)=z_1$.
In this definition, the pair of ...
3
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2
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289
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It is formally correct to say the elements of a vector space are vectors?
A vector space $\small \mathbb V$ is the association of a set of vectors and a set of scalars (or a field), e.g:
$\small \mathbb R^3$ for the vectors,
$\small \mathbb R$ for the scalars,
with ...
- 435