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	<entry>
		<id>http://eng.anarchopedia.org/index.php?title=Political_Freedom&amp;diff=36881</id>
		<title>Political Freedom</title>
		<link rel="alternate" type="text/html" href="http://eng.anarchopedia.org/index.php?title=Political_Freedom&amp;diff=36881"/>
				<updated>2008-10-12T16:20:45Z</updated>
		
		<summary type="html">&lt;p&gt;K1234567890y: /* Freedom in other languages */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{popular tag|freedom}}&lt;br /&gt;
{{popular tag|liberty}}&lt;br /&gt;
{{Voice of Freedom|165314|Definitions and Goals}}&lt;br /&gt;
&lt;br /&gt;
'''Political freedom''' is the absence of interference with the sovereignty of an individual by the use of coercion or aggression. The members of a free society would have full dominion over their public and private lives.  The opposite of a free society would be a [[totalitarian]] state, which highly restricts political freedom in order to regulate almost every aspect of behavior.  In this sense â€˜freedomâ€™ refers solely to the relation of men to other men, and the only infringement on it is coercion by men.&amp;lt;ref&amp;gt;Friedrich August von Hayek, â€˜Freedom and Coercionâ€™ in David Miller (ed), Liberty (1991) pp. 80, 81.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==What freedom is not==&lt;br /&gt;
Freedom is not a legal [[constitutional right|right]], nor is it a [[privilege]]. Legal rights are the legal barriers for the state from interfering in a person's life, however, these rights can often be suspended under some circumstances (such as [[war]], [[terrorism|terrorist]] attack, or [[natural disaster]]). Privilege is something that is normally practices only by a few persons, at the expense of others. &lt;br /&gt;
&lt;br /&gt;
Freedom is a natural right.&lt;br /&gt;
&lt;br /&gt;
==Types==&lt;br /&gt;
The concept of political freedom is very closely allied with the concepts of [[civil liberties]] and '''individual rights''', which in most [[democratic]] societies is the profession characterized by various freedoms which are afforded the legal protection of the [[state]]. Some of these freedoms may include (in alphabetical order):&lt;br /&gt;
&lt;br /&gt;
*[[Freedom of assembly]]&lt;br /&gt;
*[[Freedom of association]]&lt;br /&gt;
*[[Right to arms|Freedom to bear arms]]&lt;br /&gt;
*[[Freedom of education]]&lt;br /&gt;
*[[Freedom of movement]]&lt;br /&gt;
*[[Freedom of the press]] &lt;br /&gt;
*[[Freedom of religion]]&lt;br /&gt;
*[[Freedom of speech]]&lt;br /&gt;
*[[Freedom of thought]]&lt;br /&gt;
*[[Intellectual freedom]]&lt;br /&gt;
*[[Sexual norm|Sexual freedom]]&lt;br /&gt;
*[[Suffrage]]&lt;br /&gt;
&lt;br /&gt;
==Views==&lt;br /&gt;
&lt;br /&gt;
Various groups along the [[political spectrum]] naturally differ on what they believe constitutes &amp;quot;true&amp;quot; political freedom. &lt;br /&gt;
&lt;br /&gt;
[[Left-wing politics|Left wing]] political philosophy generally couples the notion of freedom with that of [[positive liberty]], or the enabling of an individual to realize her own potential. Freedom, in this sense, may include freedom from poverty, starvation, treatable disease, and oppression, as well as freedom from force and coercion, from whomever they may issue.&lt;br /&gt;
&lt;br /&gt;
However [[Friedrich Hayek]], a well-known [[classical liberal]], criticized this as a misconception of freedom, instead emphasizing the aspects of [[negative liberty]].&lt;br /&gt;
&lt;br /&gt;
{{Quotation|the use of â€˜libertyâ€™ to describe the physical â€˜ability to do what I wantâ€™, the power to satisfy our wishes, or the extent of the choice of alternatives open to us...has been deliberately fostered as part of the socialist argument...&lt;br /&gt;
Once this identification of freedom with power is admitted, there is no limit to the sophisms by which the attractions of the word â€˜libertyâ€™ can be used to support measures which destroy individual liberty, no end to the tricks by which people can be exhorted in the name of liberty to give up their liberty. It has been with the help of this equivocation that the notion of collective power over circumstances has been substituted for that of individual liberty and that in totalitarian states liberty has been suppressed in the name of liberty.&amp;lt;ref&amp;gt;Friedrich August von Hayek, â€˜Freedom and Coercionâ€™ in David Miller (ed), Liberty (1991) pp. 80, 85-86&amp;lt;/ref&amp;gt;}} &lt;br /&gt;
&lt;br /&gt;
Hayek also famously noted&amp;lt;ref&amp;gt;Friedrich August von Hayek, The Road to Serfdom (1944) p. 14&amp;lt;/ref&amp;gt; that &amp;quot;liberty&amp;quot; and &amp;quot;freedom&amp;quot; have probably been the most abused words in recent history.&lt;br /&gt;
&lt;br /&gt;
In contrast, [[Milton Friedman]], another classical liberal, strongly incorporated the absence from coercion into his description of political freedom.&lt;br /&gt;
&lt;br /&gt;
{{Quotation|The essence of political freedom is the absence of coercion of one man by his fellow men. The fundamental danger to political freedom is the concentration of power. The existence of a large measure of power in the hands of a relatively few individuals enables them to use it to coerce their fellow men. Preservation of freedom requires either the elimination of power where that is possible or its dispersal where it cannot be eliminated.&amp;lt;ref&amp;gt;Milton Friedman, The New Liberal's Creed: Individual Freedom, Preserving Dissent Are Ultimate Goals (1961)&amp;lt;/ref&amp;gt;}} &lt;br /&gt;
&lt;br /&gt;
Many [[social anarchism|social anarchists]] see negative and positive liberty as complementary concepts of freedom. They describe the negative liberty-centric view endorsed by [[capitialists]] as &amp;quot;selfish freedom&amp;quot;. According to [http://www.spunk.org/texts/intro/faq/sp001547/secF2.html#secf22 Anarchism FAQ]&lt;br /&gt;
{{Quotation|The right-libertarian does not address or even acknowledge that the (absolute) right of private property may lead to extensive control by property owners over those who use, but do not own, property (such as workers and tenants). Thus a free-market capitalist system leads to a very selective and class-based protection of &amp;quot;rights&amp;quot; and &amp;quot;freedoms.&amp;quot; For example, under capitalism, the &amp;quot;freedom&amp;quot; of employers inevitably conflicts with the &amp;quot;freedom&amp;quot; of employees. When stockholders or their managers exercise their &amp;quot;freedom of enterprise&amp;quot; to decide how their company will operate, they violate their employee's right to decide how their labouring capacities will be utilised. In other words, under capitalism, the &amp;quot;property rights&amp;quot; of employers will conflict with and restrict the &amp;quot;human right&amp;quot; of employees to manage themselves. Capitalism allows the right of self-management only to the few, not to all. Or, alternatively, capitalism does not recognise certain human rights as universal which anarchism does.}}&lt;br /&gt;
&lt;br /&gt;
Some{{who|date=June 2008}} treat freedom as if it were almost synonymous with [[democracy]], while others{{who|date=June 2008}} see conflicts or even opposition between the two concepts. For example, some people argue that [[Iraq]] was free under [[Paul Bremer]] on the grounds that it was a rational, humanist, non-subjugating government, long before elections were held {{Fact|date=April 2007}}. Others have argued that Iraq was free under [[Saddam Hussein]] because Iraq was not a colony {{Fact|date=April 2007}}, while a third claim is that neither dictatorial nor colonial rule in Iraq are examples of political freedom.&lt;br /&gt;
&lt;br /&gt;
[[Environmentalist]]s often argue that political freedoms should include some constraint on use of [[ecosystem]]s.  They maintain there is no such thing, for instance, as &amp;quot;freedom to pollute&amp;quot; or &amp;quot;freedom to deforest&amp;quot; given that such activities create [[negative externalities]]. The popularity of [[Sport utility vehicle|SUV]]s, [[golf]], and [[urban sprawl]] has been used as evidence that some ideas of freedom and [[ecological conservation]] can clash. This leads at times to serious confrontations and clashes of [[Value (personal and cultural)|values]] reflected in advertising campaigns, e.g. that of [[PETA]] regarding [[fur]]. &lt;br /&gt;
&lt;br /&gt;
There have been numerous [[philosophy|philosophical]] debates over the nature of freedom, the claimed differences between various types of freedom, and the extent to which freedom is desirable. [[Determinism|Determinists]] argue that all human actions are pre-determined and thus freedom is an illusion. [[Isaiah Berlin]] saw a distinction between [[negative liberty]] and [[positive liberty]].&lt;br /&gt;
&lt;br /&gt;
In [[jurisprudence]], freedom is the [[right]] to determine one's own actions autonomously ; generally it is granted in those fields in which the subject has no [[obligation]]s to fulfill or [[law]]s to obey, according to the interpretation that the hypothetical natural unlimited freedom is limited by the law for some matters.&lt;br /&gt;
&lt;br /&gt;
Joseph Garcia(Not the politition) states his belief that freedom in [[politics]] is generally used as a governing tool: &amp;quot;For what we call freedom is given only to those who obey, it is then when you stand for what you believe and fight back against oppression you lose those freedoms, and when what is taken away should be your [[inalienable rights]] what choice does one have but to obey?&amp;quot;&lt;br /&gt;
&lt;br /&gt;
==Freedom in other languages==&lt;br /&gt;
{| border=&amp;quot;1&amp;quot; cellspacing=&amp;quot;0&amp;quot; cellpadding=&amp;quot;3&amp;quot; style=&amp;quot;white-space: nowrap&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! Spelling (original) !! [[English language|English]] [[transliteration]] !! [[list of languages|Language]]&lt;br /&gt;
|-&lt;br /&gt;
! !! '''hooroeah''' !! [[Arabic language|Arabic]]&lt;br /&gt;
|-&lt;br /&gt;
! '''askatasun''' &amp;lt;br/&amp;gt; '''libertate''' !! !! [[Basque language|Basque]]&lt;br /&gt;
|-&lt;br /&gt;
! '''frihed''' !! !! [[Danish language|Danish]]&lt;br /&gt;
|-&lt;br /&gt;
! '''vrijheid''' !! !! [[Dutch language|Dutch]]&lt;br /&gt;
|-&lt;br /&gt;
! '''frÃ¦lsi''' !! !! [[Faroese language|Faroese]]&lt;br /&gt;
|-&lt;br /&gt;
! '''vapaus''' !! !! [[Finnish language|Finnish]]&lt;br /&gt;
|-&lt;br /&gt;
! '''libertÃ©''' !! !! [[French language|French]]&lt;br /&gt;
|-&lt;br /&gt;
! '''Freiheit''' !! !! [[German language|German]]&lt;br /&gt;
|-&lt;br /&gt;
! '''E&amp;amp;#955;&amp;amp;#949;&amp;amp;#965;&amp;amp;#952;&amp;amp;#949;&amp;amp;#961;&amp;amp;#959;&amp;amp;#962;''' !! '''eleftheria''' !! [[Greek language|Greek]]&lt;br /&gt;
|-&lt;br /&gt;
! '''libertÃ ''' !! !! [[Italian language|Italian]]&lt;br /&gt;
|-&lt;br /&gt;
! '''kebebasan''' !! !! [[Indonesian language|Indonesian]]&lt;br /&gt;
|-&lt;br /&gt;
! '''&amp;amp;#33258;&amp;amp;#30001;''' !! '''jiy&amp;amp;#363;''', '''ziyÃ»''' !! [[Chinese language|Chinese]]&lt;br /&gt;
|-&lt;br /&gt;
! '''libertas''' !! !! [[Latin language|Latin]]&lt;br /&gt;
|-&lt;br /&gt;
! '''FrÃ¤iheet''' !! !! [[Luxembourgish language|Luxembourgish]]&lt;br /&gt;
|-&lt;br /&gt;
! '''uhuru''' !! !! [[Nigerian pidgin|Nigerian]]&lt;br /&gt;
|-&lt;br /&gt;
! '''frihet''' !! !! [[Norwegian language|Norwegian]]&lt;br /&gt;
|-&lt;br /&gt;
! '''liberdade''' !! !! [[Polish language|Polish]]&lt;br /&gt;
|-&lt;br /&gt;
! '''liberdade''' !! !! [[Portuguese language|Portuguese]]&lt;br /&gt;
|-&lt;br /&gt;
! '''libertate''' !! !! [[Romanica language|Romanica]]&lt;br /&gt;
|-&lt;br /&gt;
! '''&amp;amp;#1089;&amp;amp;#1074;&amp;amp;#1086;&amp;amp;#1073;&amp;amp;#1086;&amp;amp;#1076;&amp;amp;#1072;''' &amp;lt;br/&amp;gt; '''&amp;amp;#1074;&amp;amp;#1086;&amp;amp;#1083;&amp;amp;#1103;''' !! '''svoboda''' &amp;lt;br/&amp;gt; '''volya''' !! [[Russian language|Russian]]&lt;br /&gt;
|-&lt;br /&gt;
! '''libertad''' !! !! [[Spanish language|Spanish]]&lt;br /&gt;
|-&lt;br /&gt;
! '''frihet''' !! !! [[Swedish language|Swedish]]&lt;br /&gt;
|-&lt;br /&gt;
! '''&amp;amp;#1570;&amp;amp;#1586;&amp;amp;#1575;&amp;amp;#1583;&amp;amp;#1609;''' !! azaadi !! [[Urdu language|Urdu]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
==External links==&lt;br /&gt;
{{wikiquote|freedom}}&lt;br /&gt;
*[http://www.freedomhouse.org/template.cfm?page=1 Freedom House]&lt;br /&gt;
*[http://www.ifex.org/ International Freedom of Expression Exchange]&lt;br /&gt;
*[http://politicaltribute.com/wordpress/?page_id=642 Political Navigator] Directory of major US related political sources&lt;br /&gt;
*[http://ksghome.harvard.edu/~aabadie/povterr.pdf Poverty, Political Freedom, and the Roots of Terrorism] from Alberto Abadie â€“ Harvard University and NBER, October 2004 (pdf)&lt;br /&gt;
*[http://gsociology.icaap.org/report/polsum.html Brief review of trends in political change: freedom and conflict] Global trends&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
{{reflist}}&lt;br /&gt;
==Sayings on freedom==&lt;br /&gt;
*&amp;quot;E&amp;amp;lambda;&amp;amp;epsilon;&amp;amp;upsilon;&amp;amp;theta;&amp;amp;epsilon;&amp;amp;rho;&amp;amp;omicron;&amp;amp;sigmaf; &amp;amp;gamma; &amp;amp;theta;&amp;amp;alpha;&amp;amp;nu;&amp;amp;alpha;&amp;amp;tau;&amp;amp;omicron;&amp;amp;sigmaf;&amp;quot; (Freedom or Death!)&amp;lt;br/&amp;gt; &amp;amp;mdash;[[Crete|Cretan]] [[war cry|War cry]].&lt;br /&gt;
*&amp;quot;Give me Liberty or give me Death!&amp;quot;&amp;lt;br/&amp;gt;&amp;amp;mdash;[[Patrick Henry]]&lt;br /&gt;
*&amp;quot;Political Freedom without economic equality is a pretense, a fraud, a lie; and the workers want no lying.&amp;quot;&amp;lt;br/&amp;gt;&amp;amp;mdash;[[Mikhail Bakunin]] in [[The Red Association]] ([[1870]])&lt;br /&gt;
&lt;br /&gt;
[[Category:Political philosophy]]&lt;br /&gt;
[[Category:Freedoms]]&lt;br /&gt;
&lt;br /&gt;
[[de:Freiheit]]&lt;br /&gt;
[[fr:LibertÃ©]]&lt;br /&gt;
[[it:LibertÃ ]]&lt;br /&gt;
[[pt:Liberdade]]&lt;/div&gt;</summary>
		<author><name>K1234567890y</name></author>	</entry>

	<entry>
		<id>http://eng.anarchopedia.org/index.php?title=freedom_(political)&amp;diff=36880</id>
		<title>freedom (political)</title>
		<link rel="alternate" type="text/html" href="http://eng.anarchopedia.org/index.php?title=freedom_(political)&amp;diff=36880"/>
				<updated>2008-10-12T16:19:53Z</updated>
		
		<summary type="html">&lt;p&gt;K1234567890y: Redirecting to freedom&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;#REDIRECT [[freedom]]&lt;/div&gt;</summary>
		<author><name>K1234567890y</name></author>	</entry>

	<entry>
		<id>http://eng.anarchopedia.org/index.php?title=Integer&amp;diff=19345</id>
		<title>Integer</title>
		<link rel="alternate" type="text/html" href="http://eng.anarchopedia.org/index.php?title=Integer&amp;diff=19345"/>
				<updated>2006-09-26T09:41:02Z</updated>
		
		<summary type="html">&lt;p&gt;K1234567890y: +zh&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;The [[integer]]s are the ring of non-fractional numbers:&lt;br /&gt;
&lt;br /&gt;
:... -3, -2, -1, 0, 1, 2, 3, ...&lt;br /&gt;
&lt;br /&gt;
These are the [[natural number]]s, with the addition of their additive inverses.  In other words, the integers extend the natural numbers into an abelian group under addition.&lt;br /&gt;
&lt;br /&gt;
We can construct a model for the integers.  Start with the model of the [[natural number]]s.  Then construct two &amp;quot;flag objects&amp;quot;, using pieces of that model:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;F_1 \equiv \{0,2\} = \{\phi,\{\phi,\{\phi\}\}\}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;F_2 \equiv \{0,3\} = \{\phi,\{\phi,\{\phi\}, \{\phi, \{\phi\}\}\}\}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Our model of the natural numbers, as laid out on the&lt;br /&gt;
[[natural number]]s page, consisted of the sets&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;0 \equiv \Phi = \{\}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;1 \equiv \{0\}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;2 \equiv \{0,1\}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;3 \equiv \{0,1,2\}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
: ...&lt;br /&gt;
&lt;br /&gt;
We can see by inspection that F&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; and F&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; are not equal to any&lt;br /&gt;
of those.  We can, therefore, use the flags to ''tag'' two copies of the&lt;br /&gt;
natural numbers.  We now define the objects used in the model of the&lt;br /&gt;
integers, shown here with primes attached, to distinguish them from&lt;br /&gt;
the similar objects used in modeling the natural numbers:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;0' \equiv \{F_1\} \cup \{0\} = \{F_1, 0\}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;1' \equiv \{F_1\} \cup \{1\} = \{F_1, 1\}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;2' \equiv \{F_1\} \cup \{2\} = \{F_1, 2\}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
: ...&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;succ'(\{F_1, x\}) \equiv \{F_1, succ(x)\}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Note that we have also defined the successor function, &amp;quot;succ'&amp;quot;, with a prime attached to distinguish it from the &amp;quot;succ&amp;quot; function which operates on the natural numbers.&lt;br /&gt;
&lt;br /&gt;
In the remainder of this page, we will use &amp;lt;math&amp;gt;\mathbb{N}&amp;lt;/math&amp;gt; to refer to this set:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\mathbb{N} \equiv \{0', 1', 2', ... \}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
We will refer to members of this set as &amp;quot;nonnegative integers&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
We can now define the ''negative'' integers as:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;-1' \equiv \{F_2\} \cup \{1\} = \{F_2, -1\}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;-2' \equiv \{F_2\} \cup \{2\} = \{F_2, -2\}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;-3' \equiv \{F_2\} \cup \{3\} = \{F_2, -3\}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
: ...&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;pred'(\{F_2, x\}) \equiv \{F_2, succ(x)\}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The entire set of integers, positive, negative, and zero, will be referred to as&lt;br /&gt;
'''I'''.&lt;br /&gt;
&lt;br /&gt;
We'll need negation later so we define it now:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;-(\{F_1,n\}) \equiv \begin{cases}&lt;br /&gt;
\{F_1,n\}, \mbox{if } n = 0 \\ &lt;br /&gt;
\{F_2,n\}, \mbox{if } n \neq 0&lt;br /&gt;
\end{cases}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;-(\{F_2,n\})\, \equiv \{F_1,n\}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and we define &amp;gt; and &amp;lt;, with respect to zero ''only'', as:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;x &amp;gt; 0 \equiv x \in (\mathbb{N} - {0})&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;x &amp;lt; 0 \equiv x \in (\mathbb{I} - \mathbb{N})&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
For ''negative'' integers -- elements of '''I''' - '''N''' -- we&lt;br /&gt;
define the '''succ'''' function implicitly, by the relation:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;succ'(x) = y \equiv x = pred'(y)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
along with the special case&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;succ'(-1') \equiv 0'&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and finally we define pred' for values in &amp;lt;math&amp;gt;\mathbb{N}&amp;lt;/math&amp;gt;:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;pred'(\{F_1,x\}) \equiv \begin{cases}&lt;br /&gt;
\{F_2,1\}, &amp;amp; \mbox{if } x = 0 \\ &lt;br /&gt;
\{F_1,pred(x)\}, &amp;amp; \mbox{if } x \neq 0&lt;br /&gt;
\end{cases}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
We can now define the ''n&amp;lt;sup&amp;gt;th&amp;lt;/sup&amp;gt;'' successor to a number&lt;br /&gt;
inductively, as&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;succ'(x,n) \equiv \begin{cases}&lt;br /&gt;
x, &amp;amp; \mbox{if } n = 0 \\ &lt;br /&gt;
succ'(succ'(x),pred'(n)), &amp;amp; \mbox{if }n &amp;gt; 0 \\ &lt;br /&gt;
succ'(pred'(x),succ'(n)), &amp;amp; \mbox{if }n &amp;lt; 0 \\ &lt;br /&gt;
\end{cases}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
With these definitions in hand, we can define a general &amp;quot;&amp;lt;math&amp;gt;\leq&amp;lt;/math&amp;gt;&amp;quot; as&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;x \leq y \equiv \ \exists n \in \mathbb{N} \left ( y = succ'(x, n) \right )&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
As with the [[natural number]]s we again can define addition and multiplication&lt;br /&gt;
in the obvious way.&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;x + y \equiv succ'(x, y)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;x \cdot y \equiv \begin{cases}&lt;br /&gt;
0, &amp;amp; \mbox{if } y = 0 \\ &lt;br /&gt;
x + (x \cdot pred'(y)), &amp;amp; \mbox{if } y &amp;gt; 0 \\ &lt;br /&gt;
- (x + (x \cdot pred'(-y))), &amp;amp; \mbox{if } y &amp;lt; 0&lt;br /&gt;
\end{cases}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
This completes the basic model: We have comparisons, addition, and&lt;br /&gt;
multiplication.  The natural numbers, '''N''', are contained within our new&lt;br /&gt;
model, and comparison in the integers is clearly an extension of comparison in&lt;br /&gt;
the natural numbers.  It's also not hard to show that addition and&lt;br /&gt;
multiplication are also extensions of the same operations on the natural&lt;br /&gt;
numbers.&lt;br /&gt;
&lt;br /&gt;
We could now go on to ''prove'' the axioms which define the integers as&lt;br /&gt;
''theorems'' within our model, including particularly the fact that each integer&lt;br /&gt;
has a unique additive inverse, thus showing that '''I''' really is a model of the&lt;br /&gt;
integers.&lt;br /&gt;
&lt;br /&gt;
[[Category:Mathematics]]&lt;br /&gt;
[[zh:æ•´æ•¸]]&lt;/div&gt;</summary>
		<author><name>K1234567890y</name></author>	</entry>

	<entry>
		<id>http://eng.anarchopedia.org/index.php?title=Mathematics&amp;diff=19344</id>
		<title>Mathematics</title>
		<link rel="alternate" type="text/html" href="http://eng.anarchopedia.org/index.php?title=Mathematics&amp;diff=19344"/>
				<updated>2006-09-26T09:40:06Z</updated>
		
		<summary type="html">&lt;p&gt;K1234567890y: +zh&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Mathematics (&amp;quot;math&amp;quot;, or &amp;quot;maths&amp;quot; in England) is a big subject.&lt;br /&gt;
&lt;br /&gt;
At its most basic, math is the study of [[relational logic]]. That is, mathematicians study logical relationships in the abstract. For this reason, mathematics are used by almost every other area of scientific or pseudo-scientific study to create models which are then related to the real world. In this way, math can be said to be the bridge between philosophical logic and real-world logic.&lt;br /&gt;
&lt;br /&gt;
----&lt;br /&gt;
&lt;br /&gt;
[Mathematics] is an independant world Created out of pure intelligence. - William Wordsworth&lt;br /&gt;
&lt;br /&gt;
[[Category:Science]]&lt;br /&gt;
[[Category:Mathematics]]&lt;br /&gt;
[[zn:æ•¸å­¸]]&lt;/div&gt;</summary>
		<author><name>K1234567890y</name></author>	</entry>

	<entry>
		<id>http://eng.anarchopedia.org/index.php?title=Anarchopedia&amp;diff=19343</id>
		<title>Anarchopedia</title>
		<link rel="alternate" type="text/html" href="http://eng.anarchopedia.org/index.php?title=Anarchopedia&amp;diff=19343"/>
				<updated>2006-09-26T09:39:15Z</updated>
		
		<summary type="html">&lt;p&gt;K1234567890y: +zh interwiki&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;'''Anarchopedia''' is an [[anarchist]] [[:m:GFDL corpus access provider|GFDL corpus access provider]], somewhat like [[Wikipedia]],  [[Wikinfo]], [[Disinfopedia]], or [[Marxists.org]].&lt;br /&gt;
&lt;br /&gt;
'''Anarchopedia''' started with work at 09:27, 30 Sep [[2004]] (GMT). English Anarchopedia started with work at 00:01, 26 Nov 2004 (GMT). &lt;br /&gt;
&lt;br /&gt;
You can read some of the articles which intend to particulary describe '''Anarchopedia''':&lt;br /&gt;
&lt;br /&gt;
*[[meta:Anarchopedia:en:itself|Anarchopedia, itself]]&lt;br /&gt;
*[[meta:Anarchopedia:en:purpose|Anarchopedia, purpose]]&lt;br /&gt;
*[[meta:Anarchopedia:en:we|Anarchopedia, we]]&lt;br /&gt;
*[[meta:Anarchopedia:en:policy|Anarchopedia, policy]]&lt;br /&gt;
*[[meta:Anarchopedia:en:direct democracy|direct democracy]]&lt;br /&gt;
*[[meta:Anarchopedia:en:Sysops|sysops]]&lt;br /&gt;
*[[meta:Anarchopedia:en:Faction|factions]]&lt;br /&gt;
*[[meta:Anarchopedia:en:what Anarchopedia is not|what Anarchopedia is not]]&lt;br /&gt;
&lt;br /&gt;
See also: [[:Category:Anarchopedia projects|Anarchopedia projects]] | [[Anarchopedia:how to help|how to help Anarchopedia]]&lt;br /&gt;
&lt;br /&gt;
[[Category:Anarchopedia]]&lt;br /&gt;
[[Category:Wikis]]&lt;br /&gt;
[[zh:å®‰é‚£å…¶ç™¾ç§‘]]&lt;br /&gt;
[[fr:Anarchopedia]]&lt;br /&gt;
[[pl:Anarchopedia]]&lt;br /&gt;
[[it:Anarchopedia]]&lt;br /&gt;
[[id:Anarchopedia]]&lt;br /&gt;
[[de:Anarchopedia]]&lt;/div&gt;</summary>
		<author><name>K1234567890y</name></author>	</entry>

	<entry>
		<id>http://eng.anarchopedia.org/index.php?title=User:K1234567890y&amp;diff=19206</id>
		<title>User:K1234567890y</title>
		<link rel="alternate" type="text/html" href="http://eng.anarchopedia.org/index.php?title=User:K1234567890y&amp;diff=19206"/>
				<updated>2006-09-20T10:21:56Z</updated>
		
		<summary type="html">&lt;p&gt;K1234567890y: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;To know more information about me, please go to [http://en.wikipedia.org/wiki/User:K1234567890y here(English page)] or [http://zh.wikipedia.org/wiki/User:K1234567890y here(Chinese page)].&lt;/div&gt;</summary>
		<author><name>K1234567890y</name></author>	</entry>

	<entry>
		<id>http://eng.anarchopedia.org/index.php?title=Earth&amp;diff=19205</id>
		<title>Earth</title>
		<link rel="alternate" type="text/html" href="http://eng.anarchopedia.org/index.php?title=Earth&amp;diff=19205"/>
				<updated>2006-09-20T10:19:10Z</updated>
		
		<summary type="html">&lt;p&gt;K1234567890y: I've written an article about the earth in Chinese version of anarchopedia&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;'''Earth''' is a [[planet]] of the [[Solar system]]. Earth is moving around the [[star]] with the official name [[Sol]] but commonly reffered to as the [[Sun]]. Earth has one physical [[satellite]] with the name [[Luna]] (usually referred to as &amp;quot;the [[Moon]]&amp;quot;), however, it is argued that Earth and Moon are actaully a single system, since they both revolve around the common center of mass, rather than one around the other.&lt;br /&gt;
&lt;br /&gt;
[[Image:Earthlights (NASA &amp;amp; NOAA).jpeg|thumb|400px|right|Image of Earth from [[cosmos]], showing the [[human]] population's effect on the planet through the [[light pollution]].]]&lt;br /&gt;
&lt;br /&gt;
3/4 of Earth surface is [[water]]. [[human|Humans]] live in the rest 1/4 and have polluted it so much that it is doubtful whether [[future]] [[generation]]s will be able to live normally.&lt;br /&gt;
&lt;br /&gt;
There are many [[society|societies]] on Earth, most notable are these of [[human]]s, [[ant]]s, [[bee]]s etc.&lt;br /&gt;
&lt;br /&gt;
Earth is 1 [[astronomic unit|AU]] away from the Sun.&lt;br /&gt;
&lt;br /&gt;
[[Category:Planets]]&lt;br /&gt;
[[zh:åœ°çƒ]]&lt;/div&gt;</summary>
		<author><name>K1234567890y</name></author>	</entry>

	</feed>