https://mizugadro.mydns.jp/t/index.php?title=Mathematical_notations&feed=atom&action=historyMathematical notations - Revision history2024-03-29T10:38:18ZRevision history for this page on the wikiMediaWiki 1.31.16https://mizugadro.mydns.jp/t/index.php?title=Mathematical_notations&diff=28374&oldid=prevT: Text replacement - "\$([^\$]+)\$" to "\\(\1\\)"2019-07-30T09:47:10Z<p>Text replacement - "\$([^\$]+)\$" to "\\(\1\\)"</p>
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<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Numbers==</div></td>
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<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Basic numbers are 0 and 1.</div></td>
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<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Basic numbers are 0 and 1.</div></td>
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<td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Operation ++ is used to construct the set of [[natural number]]s; it is postulated, that for any natural number <del class="diffchange diffchange-inline">$</del>x<del class="diffchange diffchange-inline">$</del>,</div></td>
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<td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Operation ++ is used to construct the set of [[natural number]]s; it is postulated, that for any natural number <ins class="diffchange diffchange-inline">\(</ins>x<ins class="diffchange diffchange-inline">\)</ins>,</div></td>
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<td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>operation ++ is defined. The result is denoted as <del class="diffchange diffchange-inline">$</del>x++<del class="diffchange diffchange-inline">$</del> and it presumed to be also natural number.</div></td>
<td class="diff-marker">+</td>
<td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>operation ++ is defined. The result is denoted as <ins class="diffchange diffchange-inline">\(</ins>x++<ins class="diffchange diffchange-inline">\)</ins> and it presumed to be also natural number.</div></td>
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<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>With respect to these numbers, the arithmetic operations are defined. They are denoted with</div></td>
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<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>With respect to these numbers, the arithmetic operations are defined. They are denoted with</div></td>
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</table>Thttps://mizugadro.mydns.jp/t/index.php?title=Mathematical_notations&diff=14656&oldid=prevMaintenance script at 22:02, 30 November 20182018-11-30T22:02:47Z<p></p>
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</table>Maintenance scripthttps://mizugadro.mydns.jp/t/index.php?title=Mathematical_notations&diff=6702&oldid=prevT: /* Numbers */2013-07-15T05:26:46Z<p><span dir="auto"><span class="autocomment">Numbers</span></span></p>
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<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Basic numbers are 0 and 1.</div></td>
<td class="diff-marker"> </td>
<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Basic numbers are 0 and 1.</div></td>
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<td class="diff-marker">+</td>
<td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Operation ++ is used to construct the set of [[natural number]]s; it is postulated, that for any natural number $x$,</div></td>
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<td colspan="2" class="diff-empty"> </td>
<td class="diff-marker">+</td>
<td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>operation ++ is defined. The result is denoted as $x++$ and it presumed to be also natural number.</div></td>
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<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>With respect to these numbers, the arithmetic operations are defined. They are denoted with</div></td>
<td class="diff-marker"> </td>
<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>With respect to these numbers, the arithmetic operations are defined. They are denoted with</div></td>
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<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: <math>++</math> (which has ony one argument)</div></td>
<td class="diff-marker"> </td>
<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: <math>++</math> (which has ony one argument)</div></td>
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<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: <math>+</math></div></td>
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<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: <math>+</math></div></td>
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<td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>: <math><del class="diffchange diffchange-inline">*</del></math></div></td>
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<td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>: <math><ins class="diffchange diffchange-inline">\times</ins></math></div></td>
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<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: <math>\exp</math></div></td>
<td class="diff-marker"> </td>
<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: <math>\exp</math></div></td>
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<td class="diff-marker">+</td>
<td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>: [[Tetration|<math>\mathrm{tet}</math>]]</div></td>
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<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>and so on.</div></td>
<td class="diff-marker"> </td>
<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>and so on.</div></td>
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<td class="diff-marker">+</td>
<td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"></td>
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<td class="diff-marker"> </td>
<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>At least for integers, all next operation in this raw can be constructed as recurrence of operations from previous rows.</div></td>
<td class="diff-marker"> </td>
<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>At least for integers, all next operation in this raw can be constructed as recurrence of operations from previous rows.</div></td>
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<td class="diff-marker"> </td>
<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Most of conventional calculus is based on the operations summation, multiplication, exponentiation and the inverse functions.</div></td>
<td class="diff-marker"> </td>
<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Most of conventional calculus is based on the operations summation, multiplication, exponentiation and the inverse functions.</div></td>
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</table>Thttps://mizugadro.mydns.jp/t/index.php?title=Mathematical_notations&diff=6701&oldid=prevT: Created page with " '''Mathematical notation''' is a collection of several abstract writing systems used in Mathematics and in other scientific and Technolog..."2013-07-15T05:21:12Z<p>Created page with " '''Mathematical notation''' is a collection of several abstract <a href="/t/index.php?title=Writing_system&action=edit&redlink=1" class="new" title="Writing system (page does not exist)">writing systems</a> used in <a href="/t/index.php/Mathematics" title="Mathematics">Mathematics</a> and in other <a href="/t/index.php/Science" title="Science">scientific</a> and Technolog..."</p>
<p><b>New page</b></p><div><br />
'''Mathematical notation''' is a collection of several abstract [[writing system|writing systems]] used in [[Mathematics]] and in other [[Science|scientific]] and [[Technology|technical]] contexts. Mathematical notation, in its purest form, is used to express relationships between different mathematical objects. In a technical application, the same symbols and general ideas may be borrowed to describe the theoretical values of a physical quantity. In this manner, mathematical notation serves as a common language for expressing ideas and results across all scientific disciplines, regardless of spoken language.<br />
<br />
== Overview ==<br />
The basic concepts of this slang include [[grouping]], that allows to combine several objects in one.<br />
Usually, the grouping is denoted with [[parenthesis]]. Also, the parenthesis are used to indicate the argument of operations; especially, if some operations <math>A,B,C</math> from some set (called [[group]]) can be applied sequentially, one by one, in raw, for example, <math>A\Big(B\big(C(z)\big)\Big)</math>. <br />
<br />
All things mathematicians deal with are called [[object]]s, and each object is supposed to belong to some set of objects, which is either already defined, or allows some independent definition. <br />
The possibility of such independent definition is especially important in order to exclude from the consideration such things as [[set of all possible sets]] which easy lead to [[paradox]]es, at very beginning.<br />
<br />
Mathematicians like to give names to all objects they deal with. Some ot these names are so established, that they are supposed to known [[a priori]], for example, the equality, basic arithmetical operations, natural numbers, numbers e and <math>\pi</math>, etvetera. Such names form the basics of the '''mathematical notations'''. <br />
<!--<br />
Variety of such mathematical notations is numerous, but mathematicians (and especially, [[editor]]s) apply certain efforts in order to keep some standard of mathematical notations.<br />
For example, if some author needs to use characters e or <math>\pi</math> or <math>\sum</math> or <math>\prod</math> in some non-usual way, say, as variables, then this author has to present serious reasons for such a strange choice of names of variables.<br />
!--><br />
<br />
<br />
<br />
One of ways to define the set is following.<br />
<br />
One begins with a curly parenthesis <math>\{ </math>, which is part of the [[group operation]].<br />
<br />
Then one writes some letter or character, which denotes an element of the set<br />
<br />
Then one writes the character <math>\in </math> and specifies some known (standard) set, indicating the kind of elements that can be considered; for example, will it be from a set of words, from a set of animals, numbers, etc.<br />
<br />
Then one writes the character : , and lists, separating with commas, all the properties which are specific for all elements of namely this set.<br />
<br />
Such a definition should finish with the closing of the grouping, id est, a closing curly parenthesis <math>\} </math>.<br />
<br />
===Examples===<br />
With mathematical notations above, the '''upper part of the complex halfplane''' can be defined in such a way:<br />
:<math> \{ z \in \mathbb{C} : \Im(z)\ge 0 \} </math>.<br />
Similarly, the '''lower part of the complex halfplane''' can be defined as<br />
:<math> \{ z \in \mathbb{C} : \Im(z)\le 0 \} </math>.<br />
According to these definitons, real numbers belong to the upper part of the complex halfplane and also to the lower part of the complex halfplane.<br />
<br />
==Quantifiers==<br />
*<math>\forall</math> [[forall|for all]]<br />
*<math>\exist</math> there exists<br />
<br />
==Numbers==<br />
Basic numbers are 0 and 1.<br />
With respect to these numbers, the arithmetic operations are defined. They are denoted with<br />
: <math>++</math> (which has ony one argument)<br />
: <math>+</math><br />
: <math>*</math><br />
: <math>\exp</math><br />
and so on.<br />
At least for integers, all next operation in this raw can be constructed as recurrence of operations from previous rows.<br />
Most of conventional calculus is based on the operations summation, multiplication, exponentiation and the inverse functions.<br />
Some of numbers have own single-character names: 0,1,2,3,4,5,6,7,8,9. For example, <br />
: <math> 1=0++</math><br />
: <math> 2=1++</math><br />
and so on. Most of larger numbers have no single-character mames; the integer numbers are denoted using the [[positional numeral system]].<br />
The inverse operations (if exist) of basic arithmetic operations are denoted, correspondingly, with symbols<br />
: <math>--</math><br />
: <math>-</math><br />
: <math>/</math><br />
: <math>\log</math> and <math>~^*\sqrt{~}</math><br />
and so on.<br />
<br />
==References==<br />
http://en.citizendium.org/wiki/Mathematical_notations<br />
<br />
==Keywords==<br />
[[Mathematica]]<br />
[[Mathematics]]<br />
[[Physics]]<br />
[[Science]]<br />
[[Philosophy]]<br />
<br />
[[Category:Mathematica]]<br />
[[Category:Mathematics]]<br />
[[Category:Physics]]<br />
[[Category:Science]]<br />
[[Category:Sitizendium]]</div>T