Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [convention]

Use the convention tag for questions about standard, cultural practices in mathematics.

Use the convention tag to ask questions about standard practices in mathematics.

Examples include writing unknown variables as "$x$", including or excluding $0$ in the natural numbers, defining principal square roots to be positive, etc.

414 questions
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What is the arithmetic mean of no numbers?

I have two programs that both behave nearly identically: they both take in any numbers you give them and can tell you the arithmetic mean and how many numbers were given. However, when you don't give them any numbers, one says the arithmetic mean is…
Ky -
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Why is cross product defined in the way that it is?

$\mathbf{a}\times \mathbf{b}$ follows the right hand rule? Why not left hand rule? Why is it $a b \sin (x)$ times the perpendicular vector? Why is $\sin (x)$ used with the vectors but $\cos(x)$ is a scalar product? So why is cross product defined…
koe
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What could be better than base 10?

Most people use base 10; it's obviously the common notation in the modern world. However, if we could change what became the common notation, would there be a better choice? I'm aware that it very well may be that there is no intrinsically superior…
Cisplatin
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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 some uncountable indexing set e.g. some $A \subset…
Beltrame
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Starting sentences with mathematical symbols.

I apologise if this is a duplicate in any way or is too opinion-based. To what extent is it best not to start a sentence with a mathematical symbol? I find that when trying to solve a problem or prove something it's an unnecessary distraction to…
Shaun
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5 answers

Is there a fundamental reason that $\int_b^a = -\int_a^b$

Is there a fundamental reason that switching the order of the limits in an integral results in the negative, i.e., $$\int_b^af(x)\,dx = -\int_a^bf(x)\,dx?$$ As far as I can tell, this is just chosen as a convention so that the rule…
asmeurer
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Why eliminate radicals in the denominator? [rationalizing the denominator]

Why do all school algebra texts define simplest form for expressions with radicals to not allow a radical in the denominator. For the classic example, $1/\sqrt{3}$ needs to be "simplified" to $\sqrt{3}/3$. Is there a mathematical or other…
David Lewis
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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 thing : somebody answer : "yes", somebody answer :…
Mauro ALLEGRANZA
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Why do we (mostly) restrict ourselves to Latin and Greek symbols?

99% of variables, constants, etc. that I run into are named for either a Latin character (like $x$) or a Greek character (e.g. $\pi$). Sometimes I twitch a little when I have to keep two separate meanings for a symbol in my head at once. Back…
JesseTG
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Obtaining the $\frac{1}{2\pi}$ factor in the Fourier transform

This MathWorld page gives this definition of a Fourier transform: $$F(k) = \int_{-\infty}^{\infty} f(x) e^{-2\pi i k x}dx.$$ But, I wish to speak in terms of linear frequency $\nu$ and time $t$ rather than in terms of wavenumber $k$ and position…
Andrew
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Why are the order-of-operations conventions good?

Children are sometimes taught silly mnemonics like "PEMDAS" to remember conventions on order of operations. (I never heard of "PEMDAS" until long after graduating from college, as far as I can recall. I think it means (1) parentheses, (2)…
Michael Hardy
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The convention for speakers to refer to themselves at the board with a single initial

This question is being asked on behalf of a graduate student in my department. When and where did the tradition start of a seminar or colloquium speaker using just the first initial of the speaker's last name (or initials for the speaker's first…
KCd
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Is it bad form to let the constant of integration equal several different values over a calculation

In college and later the first year of university(Engineering), I was taught that you can multiply the constant of integration by a constant value and it doesn't change, like in these examples: $$ y = \frac{1}{5}\int dx = \frac{x+C}{5} = \frac{x}{5}…
Flyingfirepig
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Are column vectors considered the "default" orientation in linear algebra?

I am taking an online course where vectors are typically written out as column vectors. It seems like the only row vectors we have seen are the transposes of column vectors and labeled as such. So I'm wondering if mathematicians (at least those in…
Stephen
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Is there a mathematical reason why rotation in the counterclockwise direction positive and clockwise rotation negative?

This inquiry has recently come to me in my study of trigonometry and the unit circle. It was said right from the very start that counterclockwise rotation were positive while clockwise rotations are negative, and I was wondering if there was a…
hubble
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