Question on the meaning, history, and usage of mathematical symbols and notation. Please remember to mention where (book, paper, webpage, etc.) you encountered any mathematical notation you are asking about.

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20 views

Are scalar/vector fields basically just “multi-valued” functions?

Not really familiar with terminology in higher Mathematics, so I will try to use python to express my ideas instead. From Wikipedia: a scalar field associates a scalar value to every point in a ...
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1answer
16 views

Classes of exponent

I found this terminology in an a paper (link) and did not understand it's meaning. Here is the set of lines that I am talking about: For each prime $p \le g$, we remove all residue classes $\mod p$ ...
2
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1answer
56 views

Is there a mathematical symbol for “once”?

I've found a couple symbols that include the concept of once, like "the list of values which appear only once" and stuff like that. Is there a symbol that just means "once" or "one repetition" or ...
2
votes
1answer
30 views

If a word starts with a number, does capitalization apply to the first letter?

If a mathematical word begins with a number and a hyphen, such as "4-dimensional" or $3-manifold," and this word occurs at the beginning of a sentence, should you capitalize the first letter? For ...
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0answers
45 views

How does someone read this notation for a proof?

I've seen this notation in both logic and math and have yet to find a resource that talks about reading it. There's usually a line in between that intersects the two horizontally. Notation: ...
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0answers
20 views

Sum notation $\sum_{\sigma\in\{\pm 1\}^n}$?

I would like to know what the following sum notation means: $$\sum_{\sigma\in\{\pm 1\}^n}\left(\prod_{1\leq i\leq n}F(x_i^{\sigma_i})\right)$$ where $n$ is a positive integer, $x_i$ are some ...
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0answers
17 views

Notation — How do I denote the derivative of a reciprocal evaluated at some value?

Let's say I have a function $f(x)$. To denote the reciprocal, I denote it as $f(x)^{-1}$. If I want to take the derivative of that, I think it's written as $(f(x)^{-1})'$. Then if I want to have that ...
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1answer
105 views

Summation notational convention

Please correct improper notation/terminology $$\sum_{k=0}^{n-1} ar^k$$. $$\sum_{k=1}^{n} ar^{k-1}$$ As far as I can tell these both represent the same thing. It's the partial sum {$S_n$} where the ...
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1answer
3k views

What is this type of math notation called? (+ 4 5)

So I've been looking for a general name of this type of mathematics notation (google hasn't been very useful) so that I can learn more about it. Basically, the symbols are in the form of functions and ...
0
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1answer
25 views

Question about $\min(a,b)$ as a notation

What does $\min(a,b)$ mean? Does it mean that it is the minimum of the interval $(a,b)$ or is it the smaller number of the two numbers? Thanks!
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0answers
38 views

Is there a standard notation for coding finite sets of numbers as numbers?

Hajek and Pudlak Metamathematics of First-Order Arithmetic use the Ackermann encoding of hereditarily finite sets, but they use no notation for codes. They let the reader see from context when a ...
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1answer
26 views

Notation Inside the Parentheses of a Function

Using the standard notation f(x), if x is strictly 1 or 2, how would this be denoted inside the parentheses? I need to use this notation also for 3,4,5, and 6. Eventually I will need to use it for ...
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1answer
26 views

Is anyone familiar with the notation $\sigma|_M$?

I am looking at Ian Stewart's Galois Theory 4th Edition, and unsure about what the notation means. Here's the theorem that the notation is first seen, Suppose $L:K$ is a finite normal extension ...
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1answer
38 views

Use of quantors/quantifiers and variables in first-order logic.

Let $v_1,v_2,\dots,v_n$ be variables and $\beta$ the variable assignment $\beta(v_n)=2n$ for $n\geq 0$. Of the following, which are true and which false under $\beta$? $\forall v_0 \exists v_1 ...
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vote
1answer
21 views

Help with logic notation, what are $S$ and $\underline0$?

This is a more or less literal translation from German, hopefully it's understandable, it's all the information available: Let $L_N=\{\underline0,S,+,\cdot~,<\}$ be the language of the natural ...
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0answers
18 views

Correct notation for Cartesian product

I have already seen two notations for the Cartesian product of a family $\{A_{\lambda}\}_{\lambda\in\Lambda}$: ...
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1answer
26 views

Decreasing Sigma Notation Sequence

Sorry if this question may seem stupid (I am just fascinated with math), but is there anyway to have a decreasing sequence with sigma notation? Example: 160, 80, 40,...
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0answers
29 views

Understanding multiindex notation and the Sobolev Space $W^{1,p}$.

The notation comes from Evans Partial Differential Equations. From Appendix A, we are given information about multiindex notation. Assume $ u : U \rightarrow R$, $ x \in U$. (a) A vector of the ...
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3answers
47 views

Math notation question

When I do my homework,I do not understand this notation in below function. The function is Let X be a continuous random variable whose probability density function is: $$f_X(x) = 3x^21_{[0,1]}(x)$$ ...
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0answers
38 views

Dream Function For Finding the Next Prime Following $n$

Is there any standard notation for this function, or is there not because it doesn't exist? If so, what is it? If not, let $D(n)$ be the dream function for finding the distance to the next prime ...
1
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0answers
23 views

Popular symbols for disjointness relation of two sets? [duplicate]

Is there any standard or popular symbol to indicate that two set A and B are disjoint? Of course, it can be described by: But it is still way too long. Is there any popular symbol for the ...
38
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5answers
3k views

What does the symbol |_ mean?

For example . And, here is another one:
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2answers
69 views

$\log^2n$, $\log n^2$, $\log \log n$, $(\log n)^2$; What are the differences? [closed]

What is the difference between the following: $\log^2n$, $\log n^2$, $\log \log n$, $(\log n)^2$
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2answers
52 views

How is the Net Change Theorem different from Fundamental Theorem Of Calculus II

1) Fundamental Theorem Of Calculus II $$ \int_{a}^{b}f'(x) = f(b) - f(a)$$ 2) Net Change Theorem $$ \int_{a}^{b}f'(x) = f(b) - f(a)$$ They are the same, why have two?
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4answers
605 views

Is my current understanding of the fundamental of calculus correct?

My current understanding: part 1) means essentially the integral is the inverse of the derivatve $$\frac {d}{dx} \int f'(x)dx = f'(x)$$ part 2) means essentially we can calculate the integral by ...
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5answers
65 views

Why do we not include $c$ in the computation of the definite integral?

Why is it when evaluating the definite integral we commonly opt to omit the constant $c$ $$\int_1^2x^2 \, dx= \left.\frac{x^3}{3} \right|_1^2 =\frac{2^3}{3}-\frac{1^3}{3}=\frac{7}{3}$$ But when ...
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0answers
19 views

Notation for variables representing complex numbers

Is there a standard way to indicate that a variable represents a complex number? In physics, it is convenient to analyze oscillating systems using complex numbers. The authors of one popular ...
14
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3answers
2k views

What is the difference between the three types of logarithms? [closed]

In complex analysis I came across three types of logarithms namely $\ln$, $\log$ and $\text{Log}$. What is the difference between the three?
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1answer
66 views

What is more correct $2^{A}$ or $2^{|A|}$

I saw at mt notebook this: for any set $A$: $$|A|\le |2^{A}|$$ Now I'm wondering, what is the meaning of $2^A$? $A$ is not a number... It doesn't need to be: $$|A|\le |2^{|A|}|$$ or $$|A|\le ...
0
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0answers
29 views

How do I write this in sigma notation?

P(x) = 1-x P(x) = 1-(1-x) P(x) = 1-{1-(1-x)} P(x) = 1-[1-{1-(1-x)}] I want to subtract the previous function by 1 each time. How can I write that in sigma notation. The function basically ...
0
votes
1answer
17 views

Formal notation for $x=^{+}_{-}a+b$

We learned in school that the solution $x$ to the equation $x^2-2x-5=0$ is $x=1\pm\sqrt{6}$. Now if x is being defined as such, the $\pm$ really means the definition isn't expanded fully; to ...
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10answers
3k views

Is there a math function to find an element in a vector?

I would like to write mathematically, if possible, the following statement: Given a vector $x=[1,4,5,3]$ and an integer $j=3$, find the position of $j$ in $x$? How to write this mathematically? ...
4
votes
1answer
178 views

Is $ \sum_{x=1}^{\infty} \frac{1}{2^x} = 1 $ an abuse of notation?

Is $ \sum_{x=1}^{\infty} \frac{1}{2^x} = 1 $ correct or is it just a shortened way to say $ \lim_{y \to \infty } \sum_{x=1}^{y+1} \frac{1}{2^x} = 1 $ ? In a softer way of asking this question if we ...
0
votes
1answer
35 views

Looking for a proper math notation

I am not a math persona so am not familiar with proper mathematical notations. I am trying to define a function $f(\cdot)$ whose domain is a set of binary numbers $\mathbb{B}=[0,1]$ and range is a ...
0
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2answers
63 views

In algebra this notation is used a lot what does it mean?

If $p,q$ are vectors, what does $\langle p,q \rangle$ mean?
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0answers
62 views

What does superscript false mean?

I was reading a blog post and found a logic statement that read as so: $ k^⊥ → k$ Do anyone know what is mean by this statement? (I read it here: ...
0
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1answer
34 views

Greatest power of 2 less than N?

Really quick question here: What sort of formal notation could I use to denote the largest power of $2$ less than $N \in \mathbb Z$?
1
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1answer
14 views

Formal distinction between $x=a$, where a is a number, vs $x=\{a_1, a_2, …, a_n\}$ where x is a solution to an algebraic equation

Currently a high school sophomore, my math curriculum doesn't go into the formal foundations of the math we learn and I'm looking to clarify a very specific idea. (assuming we are dealing with one ...
2
votes
1answer
43 views

limit notation $x \rightarrow 1^-$?

I am looking for a clarification of the following notation: $$\lim_{x\rightarrow1^-}f(x)$$ In particular, does the $1^-$ mean that $1$ is approached from below in the limit?
3
votes
1answer
40 views

Landau Notation - Practical explanations

Someone told me this week that the Landau notation is very pratical in general in analysis. Definition : Let the function $\phi$ defined on an open set containing $x_0$.We want to compare $f$ à ...
0
votes
3answers
46 views

What the notation $A\triangle B$ means?

Reading some notes on point-set topology I saw the notation $A\triangle B$ in one exercise, without any explanation of what the notation means. In this case $A$ and $B$ are sets. To provide the full ...
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1answer
26 views

Calculating the momentum - notation issue

The question is more about notation than physics, so I'll ask it here. We know that velocity $v$ is an integral of acceleration: $v(t)=\int a(t)dt$ Momentum is $p=mv$. I'd like to derive the formula ...
2
votes
1answer
45 views

Correct typography for using Leibniz Notation

What is the correct way of writing derivatives in notation form? Should the 'd' be upright or italic, that is $\mathrm d$ or $d\,$? As an example, should we write: $$ \frac {\mathrm dy}{\mathrm ...
0
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0answers
40 views

Is this integral notation correct?

In the impulse article on Wikipedia, the mathematical derivation chapter: $$J = \int_{t_1}^{t_2} \frac{d\mathbf{p}}{dt}\, dt = \int_{p_1}^{p_2} d\mathbf{p} = \mathbf{p_2} - \mathbf{p_1} = \Delta ...
5
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1answer
45 views

Integer multiplication vs. “multiple” notation in abstract algebra

In my abstract algebra text, the author uses "multiple" notation. Say you have a field $F$ that contains $a,b$. Consider some equation like $a^2 + 2ab + b^2 = 0$. The $2ab$ is meant to be shorthand ...
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1answer
25 views

Correct notation for random variable with probability distribution

For a scientific publication I am documenting the algorithm of my computer model. The model uses the Monte Carlo method and has some random variables input. Now I would like to document that ...
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2answers
21 views

Function Space vs. Concrete Function

I need confirmation for my suspicion that Space = A $\rightarrow$ B defines the domain of all functions mapping from A to B while f : A $\rightarrow$ B defines one function out of that space. ...
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1answer
41 views

What does the notation $p/|p|$ mean in topology?

What does the notation $p/|p|$ mean in topology? I guess it's associated with boundary/restriction of a map, but don't know how it is strictly defined...
2
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1answer
33 views

What set does $x\in ^{o}$ refer to?

If: $f(x)=|x-3|$ and $g(x)=2$ Solve the inequality $|x-1|<2$ I got a solution of: $1<x<5,x\in R$ But the solution in the back the book said: $1<x<5,x\in ^{o}$ Is this a typo or ...
2
votes
3answers
53 views

Is there a difference between $\sin^2(x)$ and $\sin(x)^2$?

Is there a difference between these? Or are they the same? If they're the same, then why does $\sin^2(x)$ seem like its used more often?