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isomorphism

 [ahy-suh-mawr-fiz-uhm]  

i·so·mor·phism

   [ahy-suh-mawr-fiz-uhm]
noun
1.
the state or property of being isomorphous or isomorphic.
2.
Mathematics. a one-to-one relation onto the map between two sets, which preserves the relations existing between elements in its domain.
Origin:
1820–30; isomorph(ous) + -ism
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2012.
Cite This Source Link To isomorphism

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Isomorphism is always a great word to know.
So is exponent. Does it mean:
a symbol or number placed above and after another symbol or number to denote the power to which the latter is to be raised
to change the denomination or form, but not the value, of a fraction or polynomial
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Collins
World English Dictionary
isomorphism (ˌaɪsəʊˈmɔːfɪzəm)
 
—n
1.  biology similarity of form, as in different generations of the same life cycle
2.  chem the existence of two or more substances of different composition in a similar crystalline form
3.  maths a one-to-one correspondence between the elements of two or more sets, such as those of Arabic and Roman numerals, and between the sums or products of the elements of one of these sets and those of the equivalent elements of the other set or sets

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
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American Heritage
Medical Dictionary

isomorphism i·so·mor·phism (ī'sə-môr'fĭz'əm)
n.

  1. A similarity in form, as in organisms of different ancestry.

  2. A close similarity in the crystalline structure of two or more substances of similar chemical composition.

i'so·mor'phous adj.

The American Heritage® Stedman's Medical Dictionary
Copyright © 2002, 2001, 1995 by Houghton Mifflin Company. Published by Houghton Mifflin Company.
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American Heritage
Science Dictionary
isomorphism   (ī'sə-môr'fĭz'əm)  Pronunciation Key 

  1. Similarity in form, as in organisms of different ancestry.

  2. A one-to-one correspondence between the elements of two sets such that the result of an operation on elements of one set corresponds to the result of the analogous operation on their images in the other set.

  3. A close similarity in the crystalline structure of two or more substances of different chemical composition. Isomorphism is seen, for example, in the group of minerals known as garnets, which can vary in chemical composition but always have the same crystal structure.


The American Heritage® Science Dictionary
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
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FOLDOC
Computing Dictionary

isomorphism definition

mathematics
A bijective map between two objects which preserves, in both directions, any structure under consideration. Thus a `group isomorphism' preserves group structure; an order isomorphism (between posets) preserves the order relation, and so on. Usually it is clear from context what sort of isomorphism is intended.
(1995-03-25)

The Free On-line Dictionary of Computing, © Denis Howe 2010 http://foldoc.org
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