What would be the best way to show that if F is an infinite field and f(x) is a polynomial in F[x] and f(a)=0 for an infinite number of elements a of F, that f(x) must be the zero polynomial? It kind of just makes logical sense to me, so I can't think of a way to actually show this. please help
Hello all,
I am having trouble showing that the operation defined by f*g(f of g)= Integral[from a to b]f(x)g(x) is an inner product.
I know it must fulfill the inner product properties, which are:
x*x>=0 for all x in V
x*x=0 iff x=0
x*y=y*x for all x,y in V
x(y+z)=x*z+y*z...
Hello,
I am having trouble finding an example of a set in R^2 that is neither open nor closed. I have already shown the half open interval [0,1) is neither open nor closed, but I can't seem to find any other examples. Can someone push me in the right direction? Would x^2+ y^2<1 be open nor...