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What symbol should I use if I want to indicate that I'm 'dropping', 'removing', 'dividing out' a factor from a value? If the factor I want to remove is x from v than afterwards I want v mod x != 0.

ie: let v = 180 = 2*2*3*3*5 I want to indicate v//2 = 45 = 3*3*5

What symbol would I replace // with to indicate this. (Note: // is my own personal notation)

Tolure
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    The exponent corresponding to the prime factor $p$ is usually denoted with $v_p(n)$, so you could use $\frac{n}{p^{v_p(n)}}$ , if $p$ is "divided out" from $n$. – Peter Nov 29 '21 at 13:54
  • If $m$ divides $n$, I don't see anything wrong with writing $n/m$ as a well formed expression. – While I Am Nov 29 '21 at 14:29
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    @William, but division by $2$ doesn't divide by the highest power of $2$ dividing $n$. – Mark S. Nov 29 '21 at 16:19
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    Another approach is to "cancel" out the omitted factor(s) using a slash - e.g. $\require{cancel}\color{#c00}{\cancel{0}!}$ as here. The meaning of this slash notation is likely more easily inferred than is hat notation - since most readers are already familiar slash cancellation from grade school when cancelling common factors from fractions. – Bill Dubuque Jun 08 '22 at 18:06

1 Answers1

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I've seen "hats" placed over symbols/terms omitted in a sequence (or a repeated sum, a repeated product, etc.), such as $x_1,\,x_2,\,\ldots,\, x_{k-1},\,\widehat{x_k}, \,x_{k+1}, \,\ldots,\,x_n$ indicating that the term $x_k$ is omitted from the sequence $x_1,\, x_2,\, \ldots,\,x_n,\;$ so maybe you can use

$$v \, // \,2 \;\; = \;\; 45 \;\; = \;\; \widehat{2*2}\,*3*3*5$$

However, you should still define/explain this notation, and not assume readers will be familiar with it.

Dave L. Renfro
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