Ordinal definable set - Revision history

en>Trappist the monk: /* References */replace mr template with mr parameter in CS1 templates; using AWB

2014-09-25T12:46:01Z

References: replace mr template with mr parameter in CS1 templates; using AWB

← Older revision		Revision as of 14:46, 25 September 2014
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	~~In [[mathematics]],~~ '~~''Pythagorean addition''' is the following [[binary operation]] on the [[real number]]s:~~		I'm Mellissa and I live with my husband and our 2 children in S-Hertogenbosch, in the NB south part. My hobbies are Creative writing, Roller Derby and Games Club - Dungeons and Dragons, Monopoly, Etc..<br><br>Also visit my web-site - [http://www.datingsidorna.com/ kontaktannonser]
	~~:<math>a \oplus b = \sqrt{a^~~2~~+b^2}.</math>~~
	~~The name recalls the [[Pythagorean theorem]]~~, ~~which states that the length of the [[hypotenuse ]]of a [[right triangle]] is {{nowrap\|''a'' ⊕ ''b'',}} where ''a'' and ''b'' are~~ the ~~lengths of the other sides~~.

	~~This operation provides a simple notation and terminology when the summands~~ are ~~complicated; for example~~, ~~the [[energy~~-~~momentum relation]] in [[physics]] becomes~~
	~~:<math>E = mc^2 \oplus pc.</math>~~

	~~==Properties==~~
	~~The operation ⊕ is associative~~ and ~~commutative~~, ~~and~~
	~~:<math>\sqrt{x_1^2 + x_2^2 + \cdots + x_n^2} = x_1 \oplus x_2 \oplus \cdots \oplus x_n</math>.~~
	~~This is enough to form the real numbers into a [[commutative]] [[semigroup]]. However~~, ~~⊕ is not a [[Group (mathematics)\|group]] operation for the following reasons~~.

	~~The only element which could potentially act as an [[identity element]] is 0, since an identity ''e'' must satisfy ''e''⊕''e'' = ''e''~~. ~~This yields the equation~~ <~~math~~>~~\sqrt{2}e=e~~<~~/math~~>, but if ''e'' is nonzero that implies <math>\sqrt{2}=1</math>, so ''e'' could only be zero. Unfortunately 0 does not work as an identity element after all, since 0⊕(−1) = 1. This does indicate, however, that if the operation ⊕ is restricted to nonnegative real numbers, then 0 ''does'' act as an identity. Consequently the operation ⊕ acting on the nonnegative real numbers forms a commutative [[monoid]].

	~~==See also==~~
	*[[Euclidean distance]]
	*[~~[Hypot]] function~~

	~~==Further reading==~~
	*{{cite journal \|author=Moler, Cleve and Donald Morrison \|title=Replacing Square Roots by Pythagorean Sums \|journal=IBM Journal of Research and Development \|volume=27 \|issue=6 \|pages=577–581 \|year=1983 \|url=http://www.research.ibm.com/journal/rd/276/ibmrd2706P.pdf \|doi=10.1147/rd.276.0577 \| id = {{citeseerx\|10.1.1.90.5651}} }}.
	*{{cite journal \|first=Augustin A. \|last=Dubrulle \|title=A Class of Numerical Methods for the Computation of Pythagorean Sums \|journal=IBM Journal of Research and Development \|volume=27 \|issue=6 \|pages=582–589 \|year=1983 \|url=http://www.~~research.ibm~~.com/~~journal/rd/276/ibmrd2706Q.pdf \|doi=10.1147/rd.276.0582 \| id = {{citeseerx\|10.1.1.94.3443}} }}.~~

	~~[[Category:Binary operations]~~]

en>ChrisGualtieri: General Fixes using AWB

2013-10-25T00:19:57Z

General Fixes using AWB

@@ Line 1: / Line 1: @@
-Name: Woodrow Ronan<br>Age: 34 years old<br>Country: Belgium<br>Home town: Dinant <br>Postal code: 5500<br>Address: Blekersdijk 66<br>xunjie コスト指向の価値を重視する。
+In [[mathematics]], '''Pythagorean addition''' is the following [[binary operation]] on the [[real number]]s:
-子どもたちにとても幸せで無料の霊を着て幸せな美しい服になることです！秋のシーズンでは、
+:<math>a \oplus b = \sqrt{a^2+b^2}.</math>
-ただ非常に遊び心のあるワンピースレギンスとロングTシャツの下部をカバーしています。 [http://www.schochauer.ch/_js/r/e/mall/watch/gaga/ �����ߥ�� �rӋ] 積極的な技術革新の独自のコンセプトを変更するために、
+The name recalls the [[Pythagorean theorem]], which states that the length of the [[hypotenuse ]]of a [[right triangle]] is {{nowrap|''a'' ⊕ ''b'',}} where ''a'' and ''b'' are the lengths of the other sides.
-Here is my site ... [http://bigapplefilmfestival.com/css/shop/Duvetica.php マックスマーラ ウィークエンド]
+This operation provides a simple notation and terminology when the summands are complicated; for example, the [[energy-momentum relation]] in [[physics]] becomes

en>Helpful Pixie Bot: ISBNs (Build KG)

2012-05-11T06:19:17Z

ISBNs (Build KG)

New page

Name: Woodrow Ronan Age: 34 years old Country: Belgium Home town: Dinant Postal code: 5500 Address: Blekersdijk 66 xunjie コスト指向の価値を重視する。
子どもたちにとても幸せで無料の霊を着て幸せな美しい服になることです！秋のシーズンでは、
ただ非常に遊び心のあるワンピースレギンスとロングTシャツの下部をカバーしています。 [http://www.schochauer.ch/_js/r/e/mall/watch/gaga/ ��ߥ�� rӋ] 積極的な技術革新の独自のコンセプトを変更するために、
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と厳格な検査端子表示イメージストア店、
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グローバルネットワーク】【靴の革EUがインドの総輸出の70％を占め、
バッチで留学を行ってきました、
中国市場の広い範囲を開発するために小売パートナーで動作します。 [http://www.almondpress.org/hot/fashion/chanel.html ��ͥ �å� �ǥ˥�]

Here is my site ... [http://bigapplefilmfestival.com/css/shop/Duvetica.php マックスマーラウィークエンド]