I came across an interesting problem. I'm trying to determine if the following is a vector space, x+y=xy, kx=x(risen to power k), and I came across an interesting result. I used ax. 4 to show x+y+1=(x+y)+1=(xy)+1=1(xy)=xy=x+y. Doesn't that just seem strange that 1 is the zero vector. 1 is not even a vector let alone 0. Is there something wrong with my thinking?(adsbygoogle = window.adsbygoogle || []).push({});

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

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# Finding the zero vector

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