Does the empty set satisfy all ten vector space axioms?

Adriadne · Sep 29, 2005

Thanks for that, I was quite incorrectly equating {0} with { }.

HallsofIvy · Sep 29, 2005

Adriadne said:

Oh dear, I hope as a neophyte, I'm not making a fool of myself.
OK look. Grant me that, if the empty set is a trivial subset of V, then it must, by the definition, contain the identity. So, is there no sense, in the case that the set V is a vector space, that the zero vector can be identified with the identity?

No, I won't grant you that! Saying the empty set is a subset is not the same as saying it is a subspace!

phoenixthoth · Sep 29, 2005

Adriadne said:

Thanks for that, I was quite incorrectly equating {0} with { }.

You're welcome.

Have fun here at PF!

Adriadne · Sep 29, 2005

phoenixthoth said:

Have fun here at PF!

Ha! Be careful what you say, I have a zillion half-assed questions up my sleeve!

Does the empty set satisfy all ten vector space axioms?

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