# Recent content by aortizmena

1. ### Is this proof correct? If {u,v,w} is a basis for V then {u+v+w,v+w,w}is also a basis?

Thanks chiro, yes i know alternatives of proving the statement, i was just trying to give a proof with this alternative aproach. I know i can prove it by matrix properties, by linear independence of the vectors, and by proving <{ u , v , w }>=V<{ u+v+w , v+w , w }>. Thanks though.
2. ### Is this proof correct? If {u,v,w} is a basis for V then {u+v+w,v+w,w}is also a basis?

I thought it was implicit, that was my intention
3. ### Is this proof correct? If {u,v,w} is a basis for V then {u+v+w,v+w,w}is also a basis?

Thanks Hurkyl but isn't saying that for for any arbitrary x∈V=<{ u , v , w }> with d=a, d+e=b and d+e+f=c it implies the unique solution d=a, e=b-d=b-a , f=c-d-e=c-a-(b-a)=c-a-b+a=c-b ?
4. ### Is this proof correct? If {u,v,w} is a basis for V then {u+v+w,v+w,w}is also a basis?

Let u,v,w\in V a vector space over a field F such that u≠v≠w. If { u , v , w } is a basis for V. Prove that { u+v+w , v+w , w } is also a basis for V. Proof Let u,v,w\in V a vector space over a field F such that u≠v≠w. Let { u , v , w } be a basis for V. Because { u , v , w } its a basis...
5. ### Interesting Calc of Variations Problems

you should try ramsey's model its an aplication to economics
6. ### Best Calculus book for self-study

If you really want to learn calculus, you shoud first learn logic and how to do proofs. Then read and work on any of these authors calculus books by Spivak, Apostol or Courant for a deep formal aproach (depending on which one you like the most, you cant go wrong with this ones). And maybe (just...
7. ### Easy analysis proof help

Homework Statement Prove that D={\frac{m}{2^{n}} : n\in N , m=0,1,2,...,2^{n}} (dyatic rationals set) is dense on [0,1] , i.e. if (a,b) \subset [0,1] then (a,b) \bigcap D \neq emptyset Homework Equations The Attempt at a Solution Is it wrong if I just state that because a,b\in\Re we know...