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- Thread starter Oster
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- #2

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(If you don't, think of say a line and plane in R^3. When is their union also a vector space?)

Then try translating that image into a proof.

- #3

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[tex]u_1,\dots,u_a,v_1,\dots,v_b,w_1,\dots,w_c[/tex]

where the u's belong to U, the v's belong to V and the w's belong to the intersection (if this is not a zero dimentional space). Consider for example the vector

[tex]u_1+v_1[/tex]

This vector can't belong to the union of U and V, because the basis above is composed of linearly independent vectors. So the union of U and V is not a vector space, a contraddiction.

- #4

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Thanks a lot Petr. More questions to come soon =D

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