- #1
Aziza
- 190
- 1
According to my book, a vector space V is a set endowed with two properties:
-closure under addition
-closure under scalar multiplication
and these two properties satisfy eight axioms, one of which is:
"for all f in V there exists -f in V such that f+(-f)=0"
But then isn't this axiom redundant in describing a vector space, since we already specified that V is closed under scalar multiplication? I mean, just by closure under multiplication, we know that if f is in V, -f must be in V since -f = (-1)*f, and (-1) is a scalar..
-closure under addition
-closure under scalar multiplication
and these two properties satisfy eight axioms, one of which is:
"for all f in V there exists -f in V such that f+(-f)=0"
But then isn't this axiom redundant in describing a vector space, since we already specified that V is closed under scalar multiplication? I mean, just by closure under multiplication, we know that if f is in V, -f must be in V since -f = (-1)*f, and (-1) is a scalar..