# Tagged Questions

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### How do you represent $\Im$ and $\Re$ on paper?

Do you draw $\Im$ and $\Re$ just like they are or you write $\mathtt {Im}$ and $\mathtt{Re}$?
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### Reverse Polish notation in (abstract) algebra

If I have something like $\phi\circ \psi(x)$ this means first apply $\psi$ and then $\phi$. Going right to left is pretty contrary to my intuition. In computer science some programming languages (and ...
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### Specifying types of variables in pure mathematics and applied mathematics

In pure mathematics, we can write such as "an integer $a$ ..." to specify that $a$ is a given integer or $a$ runs through the ring of integers. But in contexts where mathematics is applied ...
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### Etiquette for proper usage of Greek letters and other notation

I've progressed to the "output" point in my mathematics career and have run into a slightly embarrassing problem while writing a paper. Clearly, certain Greek letters are suitable for some situations ...
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### How do you write an integral and why

A. Year 1 Calculus Student Approach $$F(x) = \int f(x') dx\,$$ B. Random math paper you find online approach $$F(x) = \int dx f(x') \,$$ C. Spivak $$F(x) = \int f(x) \,$$ D. ??? (Edit) ...
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### Alternatives to the notation $\|x\|$ for the norm of $x$?

For aesthetic reasons, I don't like the notation $\|x\|$ for the norm of $x$. Have any alternatives been proposed?
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### Why not defining a measure as a function on functions?

A measure $\mu$ is a function to $\left[0,\infty\right]$ on the sets belonging to a $\sigma$-algebra. Then for integrable functions $f$ the integral $\int fd\mu$ comes in, having nice properties ...
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### Which letters to use as index in sequences?

Usually the latin letters $i,j,k,l,m,n$ are used as indexes in sequences or sets with $k$ elements ($A = \{ a_1,...,a_k \}$). But when we already used all these letters is there any recommendation? ...
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### Who invented or used very first the double lined symbols $\mathbb{R},\mathbb{Q},\mathbb{N}$ etc

Who invented or used very first the double lined symbols $\mathbb{R},\mathbb{Q},\mathbb{N}$ etc. to represent the real number system, rational number system, natural number system respectively?
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### How would you change math notation? [closed]

Mathematical notation has been evolving for hundreds of years (really thousands, I guess, but most of the noteworthy examples seem to be only a few hundred years old). Sometimes we are stuck with old ...
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### Should I use the minus sign when writing papers in characteristic two

Is there any consensus regarding whether one should write both "+" and "-" or only "+" when performing computations in characteristic two fields? To give some context, I am writing my thesis, which ...
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### Name of quantity that is not invariant, but only changes in one direction

How do you call a quantity that is not an invariant, but only changes in one direction during the process? Example: The degree of the polynomials go down when Euclidean division is applied, so the ...
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### Do all mathematical symbols in LaTeX have a meaning?

I debated whether I should post this on the TeX forum or here. Mathematics seemed more appropriate. LaTeX has a ridiculous amount of symbols, including countless variations of the integral sign and ...
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### How do we pronounce this symbol $'$ for $p',q'$, etc. And why?

This symbol $'$ for $p',q'$, etc; I know $'$, it is called prum(?) or something close to that, and $p',q'$ are p prum, q prum. But what exactly is $'$ written or pronounced? Thanks. And why is that ...
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### What is the meaning of $<$ in a preorder?

Let $(P,\le)$ be a preorder, i.e. $P$ is a set and $\le$ is a relation on it that is reflexive and transitive. In this context for myself I can find two interpretations for the symbol $<$ 1) ...
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### Notation for Model-Relation of formulae with free variables

Lets assume we have a formula $\mathsf{path}(x,y)$ with free variables $x,y$, and $\mathsf{acyclic}$ with no free variables on the signature $\tau = \{E\}$ (i.e. Graphs). Informally, what the formula ...
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### Why is real part written first in complex numbers?

While expressing complex numbers as $a + \iota b$, is there a specific reason for writing the real part before the imaginary part? Who introduced this notation first? Is it a case where it just hung ...
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### How to explain why one should use lowercase letters for variable names?

How can I explain to an Algebra I student why he should use lowercase letters when naming his variables (i.e. $q =$ number of quarters $vs.$ $Q =$ number of quarters? I am not interested in the ...
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### Quick question about notation and pronunciation of indices: (i+1)st or (i+1)th?

I have a somewhat silly question: What are you calling the index after the $i$th index? The $i+1$st or the $i+1$th? How do you pronounce it and how do you write it down? I like to write $i+1$ in ...
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