Predicate transformer semantics: Difference between revisions

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{{other uses|∅ (disambiguation)}}
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[[Image:SlashedZeros.svg|250px|thumb|right|Display of zero in three typefaces. From top to bottom: slashed zero, dotted zero, plain zero.]]
The '''slashed zero''' is a representation of the number '[[0 (number)|0]]' (zero), with a [[Slash (punctuation)|slash]] through it. In [[character encoding]] terms, it is an alternate [[glyph]] (in addition to the open zero glyph) for the self-same zero [[character (computing)|character]]. Unlike in the [[Scandinavian language|Scandinavian]] [[vowel]] '[[Ø]]' and the "[[empty set]]" symbol '[[∅]]', the slash of a slashed zero usually does not extend past the ellipse in most typographic designs. However the slashed zero is sometimes approximated by overlaying zero and slash characters, producing the character "<span style="font-family:Code2000" class="Unicode"><big>0̸"</big></span>.


The slashed zero glyph is often used to distinguish the digit "zero" ("0") from the [[Latin script]] letter "O" anywhere that the distinction needs emphasis, particularly in [[encoding]] systems, scientific and engineering applications, [[computer programming]] (such as [[software development]]), and telecommunications.
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==Origins==
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The slashed zero
* long predates computers, known to have been used in the twelfth and thirteenth centuries.<ref>{{harvnb|Cajori|1928}}.</ref>
* is used in many [[Baudot code|Baudot]] [[teleprinter]] applications, specifically the keytop and typepallet that combines "P" and slashed zero.<ref>"Teletype Printing Telegraph Systems, Keytops and Typepallets", Bulletin 1164B, April 1958: 1-6, Teletype part number 99564(keytop)</ref>
* is used in many ASCII graphic sets descended from the default typewheel on the [[Teletype Model 33]].<ref>Teletype Parts Bulletin 1184B pages 27 - 29 figure 29 - 31</ref>


== Usage ==
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The slashed zero, sometimes called communications zero, was used on teleprinter circuits for weather applications.<ref>"Reference Data For Radio Engineers, Fifth Edition, Howard W. Sams & Co., Inc., 1970: 30-38 Table 23</ref>


The slashed zero can be used in [[stoichiometry]] to avoid confusion with the symbol for [[Oxygen]] (capital O).
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The slashed zero symbol is widely used in video games and software product keys, and any other instance when clarity is necessary.
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The slashed zero is used by programmers in order to avoid confusion with the character 'O', when it is understood by context that a string should represent a numeric value it may be used to indicate [[null (mathematics)|null]].
 
The slashed zero is also common for recording [[amateur radio]] call signs in logs of contacts to distinguish a zero (i.e. Ø) from a capital 'O', since amateur radio call signs contain both letters and numerals.
 
When personal computers started to become mainstream in the early 1980s, it became one of the things associated with the [[hacker culture]] of the time. Some cartoons depicted computer users talking in [[binary code]] with 1s and 0s using a ''slashed zero'' for the 0.
 
Slashed zeroes can also be used on cheques in order to prevent fraud, for example: changing a 0 to an 8.
 
Slashed zeroes were once common in military radio where the problem arose of "0(zero)" being confused with "O(capital O)". On typewriters, typists would type a normal zero, backspace, and hit the slash key to mark the zero.
 
The use of the slashed zero by many computer systems of the 1970s and 1980s inspired the 1980s [[space rock]] band [[Underground Zerø]] to use the [[Scandinavian language|Scandinavian]] [[vowel]] ''[[ø]]'' in the band's name and as the band Logo on all their album covers (see link below)
 
Slashed zeroes have been used in the [[Adobe Flash|Flash-based]] artwork of [[Young-Hae Chang Heavy Industries]], notably in their 2003 work, Operation Nukorea. The reason for their use is unknown, but has been conjectured to be related to themes of 'negation, erasure, and absence'.<ref>http://www.metafilter.com/25220/That-gentle-piano-is-the-peace-of-the-grave#476182</ref>
 
== Representation in Unicode and HTML ==
{{SpecialChars}}
The treatment of slashed zero as a [[glyph]] is supported by any font whose designer chose the option. Successful display on any local system depends on having the font available there, either via the system's font files or via [[font embedding]].
 
The treatment of slashed zero with distinct [[character encoding]] is supported by [[Unicode]], but only via a pair of [[combining character]]s, not as a distinct single character (or ''[[codepoint]]'', in Unicode parlance). It is treated literally as "a zero that is slashed" and it is coded as two characters, the commonplace zero and then the "combining long solidus overlay" <code>(U+0338)</code>. These combining characters overlay the preceding character, creating a composite glyph.
 
When used in [[HTML]], use of such combining characters is valid but not yet supported by all current web browsers; for instance, [[Microsoft Internet Explorer]] fails to render them.  They may be coded as <big><code><nowiki>0&amp;#x0338;</nowiki></code></big> giving <span style="font-family:Code2000" class="Unicode"><big>0̸</big></span>.
 
==Similar symbols==
The ''slashed zero'' has the disadvantage that it can be confused with several other symbols:
 
* The ''slashed zero'' format causes problems for certain [[Scandinavian languages]] &mdash; [[Ø]] is used as a [[Letter (alphabet)|letter]] in the [[Danish alphabet|Danish]], [[Faroese alphabet|Faroese]] and [[Norwegian alphabet]]s, where it represents {{IPAblink|ø}} or {{IPAblink|œ}}.
* It also resembles the [[Greek alphabet|Greek letters]] [[Theta (letter)|Theta]] and [[Phi (letter)|Phi]] in some fonts (although usually, the slash is horizontal or vertical, respectively).
* The symbols [[Ø]] and "∅" (U+2205) are used in [[mathematics]] to refer to the [[empty set]]. <!-- &empty; ? <math>\varnothing</math> ? <math>\emptyset</math>? -->
* "{{unicode|⌀}}" (U+2300) is Unicode's codepoint for the [[diameter]] symbol.
* In German-speaking countries, Ø is also used as a symbol for [[average]] value: average in German is ''[[:de:Durchschnitt|Durchschnitt]]'', directly translated as ''cut-through''.
 
However the ''unslashed zero'' has the disadvantage that it is easily confused with the letter 'O'.
 
In paper writing one may not distinguish the 0 and O at all, or may add a slash across it in order to show the difference, although this sometimes causes ambiguity in regard to the symbol for the [[empty set]].
 
==Variations==
 
===Dotted zero===
The zero with a dot in the center seems to have originated as an option on [[IBM 3270]] display controllers. The dotted zero may appear similar to the [[Greek alphabet|Greek letter]] [[theta]] (particularly capital theta, Θ), but the two have different [[glyphs]]. In [[Raster graphics|raster]] fonts, the theta usually has a horizontal line connecting, or nearly touching, the sides of an O; while the dotted zero simply has a dot in the middle. However, on a low-definition display, such a form can be confused with a numeral 8.
 
Alternatively, the dot can become a vertical trace, for example by adding a “combining short vertical line overlay” <code>(U+20D3)</code>. It may be coded as <big><code><nowiki>0&amp;#x20D3;</nowiki></code></big> giving <span style="font-family:Code2000" class="Unicode">0⃓</span></big>.
 
===Slashed 'O'===
[[IBM]] (and a few other early mainframe makers) used a convention in which the letter O has a slash and the digit 0 does not. This is even more problematic for [[Danish people|Danes]], [[Faroese people|Faroese]], and [[Norwegian people|Norwegians]] because it means two of their letters—the '''O''' and slashed O ('''[[Ø]]''')—are similar.
 
===Reversed slash===
Some [[Burroughs Corporation|Burroughs]]/[[Unisys]] equipment displays a zero with a ''reversed'' slash, as “<span class="Unicode">&#8416;</span>".
 
===Other===
[[Image:Deutsches Kfz-Kennzeichen für Behördenfahrzeuge (Nummernbereich 3).jpg|German license plate depicting diagonal gap|thumb|right]]
Yet another convention common on early line [[computer printer|printer]]s left zero unornamented but added a tail or hook to the letter-O so that it resembled an inverted [[Q]] or [[cursive]] capital letter-O. In the [[Fixedsys]] typeface, the numeral 0 has two internal barbs along the lines of the slash, which can alternately be considered a narrow “S” within the zero. On [[Vehicle registration plates of Germany|German car license plates]], which use the [[FE-Schrift]] typeface, there is an “insinuated” slash in zeros:  a diagonal crack just beneath the top right curvature of the zero.
 
==Typefaces==
There are very few [[typeface]]s commonly included in a [[Personal Computer|PC]] that use the slashed zero.  They include:
* [[Terminal (typeface)|Terminal]] in [[Microsoft]]'s [[Windows]] line.
* [[Consolas]] in [[Microsoft|Microsoft's]] [[Windows Vista]], [[Windows 7]], [[Microsoft Office 2007]] and [[Visual Studio|Microsoft Visual Studio 2010]]
* [[Menlo (typeface)|Menlo]] in [[OS X]]
* [[Monaco (typeface)|Monaco]] in [[OS X]]
* The Linux distribution known as [[Fedora (operating system)|Fedora]] ships with a tweaked variant of the Liberation typeface which features the use of a slashed zero; this is not present on most existing Linux distributions.
* The [[DejaVu fonts|DejaVu]] family of typefaces has a "DejaVu Sans Mono" variant with a dotted zero.<ref>{{cite web
| url = http://sixrevisions.com/web_design/a-web-designers-guide-to-linux-fonts/
| title = A Web Designer's Guide to Linux Fonts
| first = Michael | last = Tuck | date = 2010-08-03 | work = Six Revisions
}}</ref>
 
==See also==
* [[0 (number)]]
* [[Symbols for zero]]
* [[Names for the number 0 in English]]
 
==Notes==
<references />
 
==References==
* {{citation| first = Florian | last = Cajori | author-link = Florian Cajori | title = A History of Mathematical Notations | location = Chicago, IL | publisher = Open Court Pub. | year = 1928–29}}; {{citation | title = op. cit. | publication-place = New York | publisher = Dover Publications | year = 1993 | isbn = 0-486-67766-4}}.
 
==External links==
* {{citation | url = http://www.catb.org/~esr/jargon/html/0/numeral-zero.html | chapter = '''0''' | title = The Jargon File | publisher = Eric S Raymond}}.
* [http://2.bp.blogspot.com/_VfTYpLOGZ3w/Sx7Qq2NSF1I/AAAAAAAAEpo/0wyq40rXrzY/s1600-h/1.jpg Underground Zerø Album Cover] Underground Zerø Band Logo
 
[[Category:Typographical symbols]]
[[Category:Numeral systems]]
[[Category:Zero]]

Latest revision as of 19:53, 4 October 2014

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