# Tagged Questions

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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### Why do mathematicians use single-letter variables?

I have much more experience programming than I do with advanced mathematics, so perhaps this is just a comfort thing with me, but I often get frustrated trying to follow mathematical notation. ...
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### Most ambiguous and inconsistent phrases and notations in maths

What are some examples of notations and words in maths which have been overused or abused to the point of them being almost completely ambiguous when presented in new contexts? For instance, a ...
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### What are some examples of notation that really improved mathematics? [closed]

I've always felt that the concise, suggestive nature of the written language of mathematics is one of the reasons it can be so powerful. Off the top of my head I can think of a few notational ...
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### What did Alan Turing mean when he said he didn't fully understand dy/dx?

Alan Turing's notebook has recently been sold at an auction house in London. In it he says this: Written out: The Leibniz notation $\frac{\mathrm{d}y}{\mathrm{d}x}$ I find extremely difficult ...
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### Why does mathematical convention deal so ineptly with multisets?

Many statements of mathematics are phrased most naturally in terms of multisets. For example: Every positive integer can be uniquely expressed as the product of a multiset of primes. But this ...
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### How Do You Actually Do Your Mathematics?

Better yet, what I'm asking is how do you actually write your mathematics? I think I need to give brief background: Through most of my childhood, I'd considered myself pretty good at math, up ...
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### Is arrow notation for vectors “not mathematically mature”?

Assuming that we can't bold our variables (say, we're writing math as opposed to typing it), is it "not mathematically mature" to put an arrow over a vector? I ask this because in my linear algebra ...
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### Why is 'abuse of notation' tolerated?

I've personally tripped up on a few concepts that came down to an abuse of notation, and I've read of plenty more on stack exchange. It seems to all be forgiven with a wave of the hand. Why do we ...
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### Why does the symbol for the multiplication operation change shape?

Why does the "$\times$" used in arithmetic change to a "$\cdot$" as we progress through education? The symbol seems to only be ambiguous because of the variable $x$; however, we wouldn't have chosen ...
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### What is “Bra” and “Ket” notation and how does it relate to Hilbert spaces?

This is my first semester of quantum mechanics and higher mathematics and I am completely lost. I have tried to find help at my university, browsed similar questions on this site, looked at my ...
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### Symbol for “probably equal to” (barring pathology)?

I am writing lecture notes for an applied statistical mechanics course and often need to express the notion that something is very probably true for functional forms found in the wild, without ...
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### Notations that are mnemonic outside of English

Some conventional math notations seem arbitrary to English speakers but were mnemonic to non-English speakers who started them. To give a simple example, Z is the symbol for integers because of the ...
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### Have there been efforts to introduce non Greek or Latin alphabets into mathematics?

As a physics student, often I find when doing blackboard problems, the lecturer will struggle to find a good variable name for a variable e.g. "Oh, I cannot use B for this matrix, that's the magnetic ...
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### Alternative notation for exponents, logs and roots?

If we have $$x^y = z$$ then we know that $$\sqrt[y]{z} = x$$ and $$\log_x{z} = y .$$ As a visually-oriented person I have often been dismayed that the symbols for these three operators ...
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### Much less than, what does that mean?

What exactly does $\ll$ mean? I am familiar that this symbol means much less than. ...but what exactly does "much less than" mean? (Or the corollary, $\gg$) On Wikipedia, the example they use is ...
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### Does “Doing a thing to both sides of an equation” have a name?

A two part question. 1 True or False: when working with an equation or inequality, everything that you do is either: a substitution, or an operation performed on each side Note that algebraic or ...
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### What do mathematicians mean by “equipped”

I am a mathematical illiterate so I do not know what people mean when they say equipped. For example, I say that Hilbert space is a vector space equipped with a inner product. What does that ...
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### What are the rules for equals signs with big-O and little-o?

This question is about asymptotic notation in general. For simplicity I will use examples about big-O notation for function growth as $n\to\infty$ (seen in algorithmic complexity), but the issues that ...
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### Are there dictionaries in math?

Consider the following dictionary in the programming language Python: D = {'A': 1, 'B': 2, 'C': 3} It is saying that the value of A is 1, the value of B is 2, ...
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### What does E mean in 9.0122222900391E-5?

I am not a mathematician(IANAM), however I wish I could be. My question: I often find this at the bottom of pages. Page generated in 0.00013899803161621 Sometimes, I come across Page ...
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### Who invented $\vee$ and $\wedge$, $\forall$ and $\exists$?

I can rather easily imagine that some mathematician/logician had the idea to symbolize "it E xists" by $\exists$ - a reversed E - and after that some other (imitative) mathematician/logician had the ...
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### Is there a sign for 'not less than', 'not greater than', etc.?

I was wondering about this, just now, because I was trying to write something like: $880$ is not greater than $950$. I am wondering this because there is a 'not equal to': $\not=$ Not equal to is an ...
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### Notation: Why write the differential first?

From reading answers here, I've noticed that some people write integrals as $\int dx \; f(x)$, while other people write them as $\int f(x)\;dx$. I realize that there is no mathematical difference ...
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### What is the accepted syntax for a negative number with an exponent?

A friend is taking a college algebra class and they are teaching him that $$-3^2 = -9$$ Their explanation is: $$-3^2 = -(3^2) = -9.$$ It has been a long time for me but I thought that in the ...
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### Is $\exp(x)$ the same as $e^x$?

For homework I have to find the derivative of $\text {exp}(6x^5+4x^3)$ but I am not sure if this is equivalent to $e^{6x^5+4x^3}$ If there is a difference, what do I do to calculate the derivative of ...
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### What does .9 with a line above the 9 mean?

What does this mean? $$\Large.\overline9$$ I've never seen this notation before.
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### Who named “Quotient groups”?

Who decided to call quotient groups quotient groups, and why did they choose that name? A lot of identities such as $$\frac{G/A}{B/A}\cong \frac{G}{B}$$ suggest that whoever invented the notation ...
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### Symbol for elementwise multiplication of vectors

This is a notation question. Assume one is given two vector $\mathbf{a}$ and $\mathbf{b}$, and one constructs a third vector $\mathbf{c}$ whose elements are given by $$c_k=a_k b_k$$ Is there any ...
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### How to represent the floor function using mathematical notation?

I'm curious as to how the floor function can be defined using mathematical notation. What I mean by this, is, instead of a word-based explanation (i.e. "The closest integer that is not greater than x"...
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### Notation for repeated application of function

If I have the function $f(x)$ and I want to apply it $n$ times, what is the notation to use? For example, would $f(f(x))$ be $f_2(x)$, $f^2(x)$, or anything less cumbersome than $f(f(x))$? This is ...
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### What is 48÷2(9+3)? [duplicate]

There is a huge debate on the internet on $48÷2(9+3)$. I figured if i wanted to know the answer this is the best place to ask. I believe it is 2 as i believe it is part of the bracket operation in ...
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### What do sine, tan, cos actually mean?

I know that $\sin\theta=\frac{y}{r}$ and $\cos\theta=\frac{x}{r}$. My question is: is $\sin$ a function of $\theta$, as in $\sin (\theta$)? If yes, why is there no $\theta$ on the right hand side of ...
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### What is the meaning of the double turnstile symbol ($\models$)?

What's the meaning of the double turnstile symbol in logic or mathematical notation? : $\models$
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### Math symbol in German thesis from 1963

I have the following math symbol in a German thesis written in 1963. Is it anything more than just a function name? It is used in the following context and then goes on to state that "If the ...
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### The formalism behind integration by substitution

When you are doing an integration by substitution you do the following working. \begin{align*} u&=f(x)\\ \Rightarrow\frac{du}{dx}&=f^{\prime}(x)\\ \Rightarrow du&=f^{\prime}(x)dx&(1)\...
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### Why do we use “congruent to” instead of equal to?

I'm more familiar with the notation $a \equiv b \pmod c$, but I think this is equivalent to $a \bmod c = b \bmod c$, which makes it clear that we should put a $=$ instead of $\equiv$. What's the ...
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### What does $dx$ mean?

$dx$ appears in differential equations, such us derivatives and integrals. For example, a function $f(x)$ its first derivative is $\dfrac{d}{dx}f(x)$ and its integral $\displaystyle\int f(x)dx$. But ...
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### Why does drawing $\square$ mean the end of a proof?

To end a proof, I often write "as was to be shown" or "q.e.d". Both of these terms make sense to me as a reader. On the other hand, I feel a little strange to put down $\square$ although I saw it ...
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