12-240/Classnotes for Tuesday September 18: Difference between revisions
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Recap: |
Recap: |
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Thrm: In a field F: |
Thrm: In a field F: |
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1. a+b = c+b |
1. a+b = c+b => a=c |
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2. b≠0, a∙b=c∙b => a=c |
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3. 0 is unique. |
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4. 1 is unique. |
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5. -a is unique. |
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6. a^-1 is unique (a≠0) |
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7. -(-a)=a |
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8. (a^-1)^-1 =a |
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9. a∙0=0 **Surprisingly difficult, required distributivity. |
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10. ∄ 0^-1, aka, ∄ b∈F s.t 0∙b=1 |
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11. (-a)∙(-b)=a∙b |
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Revision as of 21:55, 18 September 2012
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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
