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What is the difference between nouns "size" and "dimension". When I want to set dimensions/sizes of an object which noun should I use?

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You can find both words in most of dictionaries. As a physicist I would not use the word "dimension" in daily life. For me, this is a mathematical term designated a property of space. The noun "size" refers to geometrical properties of surrounding us objects. Below are some daily meanings of the noun "dimension" fom dictionary.com.

a. measurement in length, width, and thickness.

b. scope; importance: the dimensions of a problem.

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Dimension means size for engineering, formally or informally, and has a vector property associated with it. One can refer to the dimension "length" of a couch when buying furniture or on a mechanical drawing designing it. "Size" is more general. The words are synonyms; it is the usage which differs. I must disagree with our physicist friend regarding the use of the word dimension in ordinary speech. People use it all the time when they are specifying the length property of day-to-day objects, especially how they will fit into a given space.

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I'll plan to use this term for describing object geometry, that's why I preffer the physical or mathematical meaning: "geometrical properties of surrounding us objects". But your opinion is usefull too. –  Ivan Z Apr 22 '13 at 9:44

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