Question

Can somebody please prove a+(-a)=0

Answer 1

A number + it's negation = 0?

Answer 2

i believe its an axiom; and axioms need no proof

Answer 3

Yes, this the definition of what -a means. In the standard axiomatic definition of the real numbers there is an axiom that states

For every real number x, there is another real number y such that x + y = 0.

And we write y = -x

Answer 4

Perhaps some further clarification would help.

I am trying to prove the following:

Define V=span{v1,v2} and S=span{s1,s2}.
Suppose W = { x | x = v + s, forall v in V, s in S }. Is W a Vector space?

Using the axioms of what a vector space is, if I cannot prove that there exists -x such that x + ( -x ) = 0, how can I prove it is a vector space?

Answer 5

Ok.

But this is easy to prove. First note that V and S are themselves subspaces.

Then for any x in W, there is a v in V and and s in S such that x = v + s

As V and S are themselves subspaces, =v and -s are members of V and S respectively and the vector y = -v + -s is the additive inverse of x.

Answer 6

that should be "-v and -s are members ..."

Answer 7

Thanks mate

Answer 8

Kein Problem!

Answer 9

= sure thing