- #1
TranscendArcu
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Homework Statement
Prove that [itex]\vec0 + \vec{A} = \vec{A}[/itex]
The Attempt at a Solution
[tex]\vec{A} + (-\vec{A}) = \vec0[/tex]
[tex]\vec0 + \vec{A} = \vec{A} + (-\vec{A}) + \vec{A} = \vec{A} + \vec{A} + (- \vec{A})[/tex]
[tex]\vec0+ \vec{A} = \vec{A} + \vec0 = \vec{A}[/tex]
I find this last line somewhat unconvincing since it seems it could also be retrieved by the axiom [itex] \vec{A} + \vec{B} = \vec{B} + \vec{A}[/itex]. Is this a legitimate proof or do I have to do this another way?