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 Post subject: Vector spacePosted: Mon, 16 Jul 2012 22:48:30 UTC
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Question : Is the set Q of rational numbers a real vector space (i.e. scalars are the real

Yes, since all rational numbers are real numbers?

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 Post subject: Re: Vector spacePosted: Tue, 17 Jul 2012 02:42:50 UTC
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johndoe wrote:
Question : Is the set Q of rational numbers a real vector space (i.e. scalars are the real

Yes, since all rational numbers are real numbers?

In , can you multiply by, e.g. ?

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 Post subject: Re: Vector spacePosted: Tue, 17 Jul 2012 03:47:31 UTC
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johndoe wrote:
Question : Is the set Q of rational numbers a real vector space (i.e. scalars are the real

Yes, since all rational numbers are real numbers?

You need that real times rational is rational...

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 Post subject: Re: Vector spacePosted: Tue, 17 Jul 2012 17:02:31 UTC
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outermeasure wrote:
johndoe wrote:
Question : Is the set Q of rational numbers a real vector space (i.e. scalars are the real

Yes, since all rational numbers are real numbers?

In , can you multiply by, e.g. ?

o so no, since I get irrational numbers after certain axiom operations.

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 Post subject: Re: Vector spacePosted: Wed, 18 Jul 2012 04:52:07 UTC
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johndoe wrote:
outermeasure wrote:
johndoe wrote:
Question : Is the set Q of rational numbers a real vector space (i.e. scalars are the real

Yes, since all rational numbers are real numbers?

In , can you multiply by, e.g. ?

o so no, since I get irrational numbers after certain axiom operations.

What axiom operations? You mean that there is no closure under the field action.

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 Post subject: Re: Vector spacePosted: Wed, 18 Jul 2012 15:40:59 UTC
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Joined: Mon, 10 Mar 2008 04:43:48 UTC
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Location: Autistic nation
johndoe wrote:
outermeasure wrote:
johndoe wrote:
Question : Is the set Q of rational numbers a real vector space (i.e. scalars are the real

Yes, since all rational numbers are real numbers?

In , can you multiply by, e.g. ?

o so no, since I get irrational numbers after certain axiom operations.

What axiom operations? You mean that there is no closure under the field action.

That I mean I engage in all those associativity, commutativity.. properties.

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 Post subject: Re: Vector spacePosted: Wed, 18 Jul 2012 18:49:37 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
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johndoe wrote:
johndoe wrote:
outermeasure wrote:
johndoe wrote:
Question : Is the set Q of rational numbers a real vector space (i.e. scalars are the real

Yes, since all rational numbers are real numbers?

In , can you multiply by, e.g. ?

o so no, since I get irrational numbers after certain axiom operations.

What axiom operations? You mean that there is no closure under the field action.

That I mean I engage in all those associativity, commutativity.. properties.

I'm a little confused, why are you thinking about associativity and commutativity? Those are fine, and is a field, so those will all work fine, it's closure that's the issue.

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