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{{Other uses|Distinction (disambiguation)}}
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Two or more things are '''distinct''' if no two of them are the same thing. In [[mathematics]], two things are called '''distinct''' if they are not [[equality (mathematics)|equal]]. In [[physics]] two things are distinct if they cannot be [[Topology|mapped]] to each other.<ref>{{Cite book|author=Martin, Keye|year=2010|chapter=Chapter 9: Domain Theory and Measurement: 9.6 Forms of Process Evolution|title=New Structures for Physics|series=Volume 813 of Lecture Notes in Physics|editor=Coecke, Bob|location=Heidelberg, Germany|publisher=Springer Verlag|pages=579&ndash;580|isbn=978-3-642-12820-2}}</ref>


==Species or classes==
Think about it this way. Someone has the address of Ann Arbor, MI (my hometown, GO BLUE!) on a slip of paper called "annArborLocation". You copy it down on a piece of paper called "myDestination". You can drive to "myDestination" and plant a tree. You may have changed something about the city at that location, but it doesn change the LAT/LON that was written on either paper. You can change the LAT/LON on "myDestination" but it doesn change "annArborLocation". Thanks! May I humbly suggest a little addition: you should mention that there is actually a specific term that describes this form of "call by value [http://www.clounagh.com/booking/classes/fold.php?lv=50 Louis Vuitton Trainers Replica] where the value is a reference" that was invented by Barbara Liskov for describing the evaluation strategy of her CLU language in 1974, in order to avoid confusion such as the one your article addresses: call by sharing (sometimes called call by object sharing or simply call by object), which pretty much perfectly describes the semantics. But, also, if you see someone accepting Java as pass by value, I can show code that breaks that theory, based on their weak higher level understanding of "pass by value". The terminology is at fault here. Java and 'p' cannot be written in the same book, forum, or even txt.<br><br>I, OTOH, read and prefer print newspapers and magazines. Just last month I finally went to a [http://www.homebakedimages.com/portfolio/travel/upload.asp?a=16-Nike-Cortez-Shoes Nike Cortez Shoes] digital subscription for the New York Times but did so for 2 reasons: (1) it saved me $100 on the Nook Tablet and (2) the digital subscription cost less than one half of the print subscription and promised more timely delivery.<br><br>My dow does not stick to the blade as with a knife or a plasitc dow cutters.I like how I can use the tool to chop vegitable easily and quickly with out worring about them moving. Its edge is cut super straight, no weird bowing to it, which might not seem like a huge deal until you think about how it could be subpar and always make slightly rounded cuts or the kind of cuts that don't go all the way through in the middle  but it's a gem and does neither of those things. <br><br>YouTube and the printing press have changed society in a few [http://www.aquila-tc.co.uk/competitions/header.asp?p=121-Buy-Jeremy-Scott-Adidas-Uk Buy Jeremy Scott Adidas Uk] ways. Firstly there has been a way to preserve the knowledge that we have, through the permanence of the Internet as well as the archiving abilities of the printed word. Secondly we are more aware of world affairs, it is important to understand that world affairs may not affect us now but could in the near future due to the interdependence of countries in the 21st Century, this is not just an issue for the concerns YouTube with its real time updates but [http://www.silverglitzbengals.co.uk/confuse/mail.asp?v=33 Vibram Bikila Ls Amazon Uk] also the printing press with regards to the information printed and distributed to the population.
{{Quote|[I]t is plain that our distinct species are nothing but distinct complex ideas, with distinct names annexed to them. It is true every substance that exists has its peculiar constitution, whereon depend those sensible qualities and powers we observe in it; but the ranking of things into species (which is nothing but sorting them under several titles) is done by us according to the ideas that we have of them: which, though sufficient to distinguish them by names, so that we may be able to discourse of them when we have them not present before us; yet if we suppose it to be done by their real internal constitutions, and that things existing are distinguished by nature into species, by real essences, according as we distinguish them into species by names, we shall be liable to great mistakes.|John Locke|An Essay Concerning Human Understanding<ref>{{Cite book|author=Locke, John|title = An Essay Concerning Human Understanding|chapter=Book 3: Chapter 6: Of the Names of Substances|url=http://www.ilt.columbia.edu/publications/Projects/digitexts/locke/understanding/chapter0306.html}}</ref>}}
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==In mathematics==
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===Example===
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A [[quadratic equation]] over the [[complex number]]s has two [[root of a function|root]]s.
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<ul>
The equation
 
 
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[[Factorization|factors]] as
 
 
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<math>(x - 1)(x - 2) = 0</math>
 
 
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and thus has as roots ''x'' = 1 and ''x'' = 2.
 
Since 1 and 2 are not equal, these roots are distinct.
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In contrast, the equation:
</ul>
 
<math>x^{2} - 2x + 1 = 0</math>
 
factors as
 
<math>(x - 1)(x - 1) = 0</math>
 
and thus has as roots ''x'' = 1 and ''x'' = 1.
Since 1 and 1 are (of course) equal, the roots are not distinct; they ''coincide''.
 
In other words, the first equation has distinct roots, while the second does not. (In the general theory, the [[discriminant]] is introduced to explain this.)
 
===Proving distinctness===
In order to [[mathematical proof|prove]] that two things ''x'' and ''y'' are distinct, it often helps to find some [[property (metaphysics)|property]] that one has but not the other.
For a simple example, if for some reason we had any doubt that the roots 1 and 2 in the above example were distinct, then we might prove this by noting that 1 is an [[odd number]] while 2 is [[even number|even]].
This would prove that 1 and 2 are distinct.
 
Along the same lines, one can prove that ''x'' and ''y'' are distinct by finding some [[function (mathematics)|function]] ''f'' and proving that ''f''(''x'') and ''f''(''y'') are distinct.
This may seem like a simple idea, and it is, but many deep results in mathematics concern when you can prove distinctness by particular methods. For example,
 
*The [[Hahn–Banach theorem]] says (among other things) that distinct elements of a [[Banach space]] can be proved to be distinct using only [[linear functional]]s.
*In [[category theory]], if ''f'' is a [[functor]] between [[Category (mathematics)|categories]] '''C''' and '''D''', then ''f'' always maps [[morphism|isomorphic]] objects to isomorphic objects. Thus, one way to show two objects of '''C''' are distinct ([[up to]] [[isomorphism]]) is to show that their images under ''f'' are distinct (i.e. not isomorphic).
<!--''I don't know what to say here, but there are issues. I can mention [[Leibniz's law]] (which we don't have an article on); this is the claim that distinct things can always be proved distinct as in the last section by some property. These ideas could be discussed under [[Identity (mathematics)|Identity]]. There is some discussion at [[Identity and change]].''
-->
 
==See also==
{{Wiktionary|distinct}}
 
==Notes==
{{Reflist}}
 
[[Category:Elementary mathematics]]

Latest revision as of 18:52, 7 November 2014

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Think about it this way. Someone has the address of Ann Arbor, MI (my hometown, GO BLUE!) on a slip of paper called "annArborLocation". You copy it down on a piece of paper called "myDestination". You can drive to "myDestination" and plant a tree. You may have changed something about the city at that location, but it doesn change the LAT/LON that was written on either paper. You can change the LAT/LON on "myDestination" but it doesn change "annArborLocation". Thanks! May I humbly suggest a little addition: you should mention that there is actually a specific term that describes this form of "call by value Louis Vuitton Trainers Replica where the value is a reference" that was invented by Barbara Liskov for describing the evaluation strategy of her CLU language in 1974, in order to avoid confusion such as the one your article addresses: call by sharing (sometimes called call by object sharing or simply call by object), which pretty much perfectly describes the semantics. But, also, if you see someone accepting Java as pass by value, I can show code that breaks that theory, based on their weak higher level understanding of "pass by value". The terminology is at fault here. Java and 'p' cannot be written in the same book, forum, or even txt.

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