Editing Slash (punctuation) (section)

==== Division <span class="anchor" id="division"></span>====
The division slash {{char|∕}} is used between two numbers to indicate [[division (math)|division]].{{efn|The [[ISO 80000]] standard says that the [[division sign]] {{char|÷}}, used in elementary schools in many [[Anglophone]] countries, "should not be used" to indicate division because in other countries it is used to indicate a range of values or negation.<ref name=ISO>ISO 80000-2, Section 9 "Operations", 2-9.6</ref>}} This use developed from the [[fraction slash]] in the late 18th or early 19th century.<ref name="jeff" /> The formatting was advocated by [[Augustus De Morgan|De Morgan]] in the mid-19th century.<ref>{{cite book |last=De Morgan |first=Augustus |author-link=Augustus De Morgan |contribution=The Calculus of Functions |title=Encyclopædia Metropolitana |date=1845 |location=London |publisher=B. Fellowes et al.}}</ref>{{full citation needed|date=September 2023|reason=Volume and page number needed.}},<ref name="DeM">{{cite web |last1=Morgan |first1=Augustus De |title=A Treatise on the Calculus of Functions (Extracted From The Encyclopædia Metropolitana) |url=https://www.google.com/books/edition/A_Treatise_on_the_Calculus_of_Functions/GoM_AAAAcAAJ?hl=en&gbpv=1&pg=PA84&printsec=frontcover&dq=division |publisher=Baldwin and Cradock |language=en |date=1836}} Page 84 in this version</ref> who wrote:
:The occurrence of fractions, such as {{sfrac|a|b}}, {{sfrac|a+b|c+d}}, in the <!-- the previous two words are difficult to decipher in the scan, but it's hard to imagine them being anything beside these two words --> verbal part of mathematical works is a source of considerable loss of room, and creates an inelegant and even confused appearance in the printed page. It is very desirable, in every point of view, except the strictly mathematical one, that some method of representation should be adopted which does not require a larger space than is usual between two successive lines. At the same time, it is by no means of very great importance that the verbal part should entirely coincide with the mathematical part in notation, so long as the latter remains to preserve the usual conventions. The symbol ÷ has been disused for a sufficient reason, namely, the number of times which the pen must be taken off to form it. This has been, and we imagine always will be, the cause either of abandonment or abbreviation. The question is, whether a new and easy notation could not be substituted; and it is desirable that it should be derived from analogy, such as (accidentally, we believe) does exist in >, =, and <. If we look at × and +, and observe that the first is made by turning the second through half a right angle, denoting multiplication, which is primarily an extension of addition in like manner as division is an extension of subtraction, we may thus invent the symbol / or \ to denote division, which is also the symbol of subtraction turned through half a right angle. If a/b were used to denote a divided by b, and (a+b)/(c+d) to denote a + b divided by c + d, all necessity for increased spacing would be avoided; but this alteration should not be introduced into completely mathematical expressions, though it would be convenient in particular cases.<ref name="DeM" />
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:A complicated exponent might be avoided by the use of the symbol λ⁻¹. The student would soon learn to consider λ⁻¹{(a+bx)/(c+ex)×λa} as meaning the same thing as <center><math>a^{\frac{a+bx}{c+ex}}</math>.</center>
:If, in the course of investigation, some plan of this kind be not adopted, the expense of printing will place a limit to analysis. A work entirely devoted to the consideration of such expressions as the preceding might easily be doubled in size and price by the frequent occurrence of them in the text, or else rendered confused and unintelligible by successive abbreviations. Considering, however, that λ is an inverse symbol in the sense of (124.), and λ⁻¹ a direct one, it would, perhaps, rather be advisable that some method of denoting an exponent should be adopted which does not raise the exponent above the symbol of the root. Either of the following might be proposed, the defect of them all being that they are not derived from analogy:
:<center>a Λ {(a+bx)/(c+ex)} a:{(a+bx)/(c+ex)},</center>
:or the like. But we do not advocate the introduction of these into purely symbolical expressions, any more than in the former case.
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