# Tagged Questions

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

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### Are these equivalent? $\cos^2(5x) = (\cos(5x))^2$

Are these equivalent? $$\cos^2(5x) = (\cos(5x))^2$$
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### Special Case of Summation

Hello what would be the solution to the summation over the range from 1 to 0? $$\sum_{1}^{0} = ?$$ My guess is -1 or 0, but I can't find any reference to this case.
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### Why do texts frequently define $\mathbf {i}$?

Often when I see a formula containing $\mathbf {i}$, it will be accompanied by the definition $\mathbf {i^2 = -1}$. Why don't we just assume that most students of advanced math know what $\mathbf {i}$ ...
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### Convention for chain of inequalities

Sorry if this is not the right place to ask. In the proof of a theorem, I basically want to write $A<B$, and $B=C$, thus $A<C$ as a chain of inequalities. I am not sure if there is a convention ...
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### Summation and Product notation: Convention for when final index number is smaller than the first?

What, for example, are the following? $\sum_{i=5}^4i$ $\prod_{i=5}^4i$ Is there a standard convention for what they should be? My guess is that $\sum_{i=5}^4i=0$ and $\prod_{i=5}^4i=1$. Is that ...
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### Choosing the definition of $\frac{\partial^2}{\partial x\partial y}$

Today, I answered this question and discovered that the definition of $\dfrac{\partial^2}{\partial x\partial y}$ is a matter of convention. For example this .edu link and this other .edu link use the ...
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### Is there a convention regarding the capitalization of adjectives derived from proper names?

Many mathematical properties are derived from the name of a mathematician associated with them: "Abelian," "Noetherian," "Artinian," "Frobenius (algebra, category, etc...)," "Cauchy," etc. It seems ...
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### Is it correct to define variables and functions that are more than one character?

Most of the time (at least at my high school student level), we are using variables such as a, b or $\theta$, and functions such as f, g etc... But would it be possible to use multiple characters ? ...
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### Rationale behind tuple notation for structured sets

Defining structured sets typically involves the convention of using a tuple of some sort; for example, the real line can be thought of as the quadruple $(\mathbf{R},+,\cdot,<)$. But this convention ...
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### Is there any convention regarding the order of operation of the binary modulo operator?

Is there any predominant convention as to where the binary modulo operator (i.e., the variant of the modulo operator that is not applied to a whole equation) ranks in the order of operations, in ...
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### Why is $0^0$ also known as indeterminate? [duplicate]

I've seen on Maths Is Fun that $0^0$ is also know as indeterminate. Seriously, when I wanted to see the value for $0^0$, it just told me it's indeterminate, but when I entered this into the exponent ...
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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 ...
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### Why is empty product defined to be $1$? [duplicate]

For example $\prod_{2 \le j < 1} 2^j= 1.$ How does that happen?
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### Question about sums with a negative limit for the index

To me, it looks like we have $\;\sum_{i = 1}^{0} x_i = 0\;$ and $\;\sum_{i = 1}^{1} x_i = x_1\;$. What happens if I write the following? $$\;\sum_{i = 1}^{-123} x_i\;$$ Would this be defined?
Let $G$ be a semisimple algebraic group over an algebraically closed field $k$, so that $G$ is an almost-direct product of its minimal closed connected normal subgroups of positive dimension, ...