- #1

- 207

- 0

## Main Question or Discussion Point

Well, I'm supposed to prove 0v=0

It is stated that I'm only allowed to use the following axioms.

let a,b,c be vectors and V is a vector space, then

1)a&b is in V then a+b is in V

2)a+b=b+a

3)a+(b+c)=(a+b)+c

4)0+a=a+0=a

5)a+(-a)=(-a)+a=0

6)a is in V implies ka is in V

7)k(a+b)=ka+kb

8)(k+m)a=ka+ma

9)k(ma)=(km)a

10) 1a=a

The book does it like this, and i think its wrong

0v=(0+0)v=0v +0v { axioms 4&8}

now subtract 0v from both sides { axioms ????}

we get 0=0v

you see the problem here? theres no justification for the subtraction step because there is no axiom allowing the step. Logically I assume that I'm only allowed to use the 10 axioms to prove this theorem.

It is stated that I'm only allowed to use the following axioms.

let a,b,c be vectors and V is a vector space, then

1)a&b is in V then a+b is in V

2)a+b=b+a

3)a+(b+c)=(a+b)+c

4)0+a=a+0=a

5)a+(-a)=(-a)+a=0

6)a is in V implies ka is in V

7)k(a+b)=ka+kb

8)(k+m)a=ka+ma

9)k(ma)=(km)a

10) 1a=a

The book does it like this, and i think its wrong

0v=(0+0)v=0v +0v { axioms 4&8}

now subtract 0v from both sides { axioms ????}

we get 0=0v

you see the problem here? theres no justification for the subtraction step because there is no axiom allowing the step. Logically I assume that I'm only allowed to use the 10 axioms to prove this theorem.