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Subspace and subset

 
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Sep24-12, 07:58 AM   #1
 

Subspace and subset

Hi,

A quick question:
Does a set need to be a subset to be a subspace of some vector space?
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Sep24-12, 08:04 AM   #2
 
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Quote by Max.Planck View Post
Hi,

A quick question:
Does a set need to be a subset to be a subspace of some vector space?
Yes, a subspace of a vector space V necessarily needs to be a subset.
Sep24-12, 08:40 AM   #3
 
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A vector space is a set of objects with "addition" and "scalar multiplication" defined. A "subspace" is a subset with the "inherited" addition and scalar multiplication.
Sep24-12, 09:22 AM   #4
 

Subspace and subset

Quote by HallsofIvy View Post
A vector space is a set of objects with "addition" and "scalar multiplication" defined. A "subspace" is a subset with the "inherited" addition and scalar multiplication.
Thank you!
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