- #1
xalvyn
- 17
- 0
Hi everyone,
I would like to seek help in proving that the vector space postulate 1.X = X cannot be derived from the other postulates, e.g. X + 0 = X, X + (Y + Z) = (X + Y) + Z.
The only hint I am given is to construct the "pseudo-scalar product"
c # X = the projection of c.X on a fixed line.
This problem is from Birkhoff and Maclane's "A Survey of Modern Algebra".
I would like to seek help in proving that the vector space postulate 1.X = X cannot be derived from the other postulates, e.g. X + 0 = X, X + (Y + Z) = (X + Y) + Z.
The only hint I am given is to construct the "pseudo-scalar product"
c # X = the projection of c.X on a fixed line.
This problem is from Birkhoff and Maclane's "A Survey of Modern Algebra".