- #1

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## Homework Statement

Establish a [itex]\bullet[/itex] 0 = 0

## Homework Equations

A few axioms I thought to be relevant..

## The Attempt at a Solution

a = a

a [itex]\bullet[/itex] 0 = 0 [itex]\bullet[/itex] a

(a [itex]\bullet[/itex] 0) - (0 [itex]\bullet[/itex] a) = 0

a(1 [itex]\bullet[/itex] 0) - a(0 [itex]\bullet[/itex] 1) = 0

a[(1 [itex]\bullet[/itex] 0) - (0 [itex]\bullet[/itex] 1)] = 0

a [itex]\bullet[/itex] 0 = 0