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  3. example 1.8. fix a domain d, and let v be the set

Example 1.8. Fix a domain D, and let V be the set of all functions f(t)...

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Advance Math

Example 1.8. Fix a domain D, and let V be the set of allfunctions f(t) defined
on D. Define addition and scalar multiples as with polynomials forall t ? D:

(f + g)(t) = f(t) + g(t)
(cf)(t) = cf(t)

Then V is a vector space as well, the axioms are verifiedsimilarly to those for Pn.

Verify that V in the previous example satisfies theaxioms for a vector space.

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