Difference between revisions of "12-240/Classnotes for Tuesday September 18"

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{{12-240/Navigation}}
 
{{12-240/Navigation}}
  
Recap:
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== Recap: ==
 
Thrm: In a field F:
 
Thrm: In a field F:
 
1. a+b = c+b => a=c
 
1. a+b = c+b => a=c

Revision as of 21:56, 18 September 2012

Recap:

Thrm: In a field F: 1. a+b = c+b => a=c 2. b≠0, a∙b=c∙b => a=c 3. 0 is unique. 4. 1 is unique. 5. -a is unique. 6. a^-1 is unique (a≠0) 7. -(-a)=a 8. (a^-1)^-1 =a 9. a∙0=0 **Surprisingly difficult, required distributivity. 10. ∄ 0^-1, aka, ∄ b∈F s.t 0∙b=1 11. (-a)∙(-b)=a∙b