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

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Thrm: In a field F:
Thrm: In a field F:
1. a+b = c+b => a=c
1. a+b = c+b => a=c

2. b≠0, a∙b=c∙b => a=c
2. b≠0, a∙b=c∙b => a=c

3. 0 is unique.
3. 0 is unique.

4. 1 is unique.
4. 1 is unique.

5. -a is unique.
5. -a is unique.

6. a^-1 is unique (a≠0)
6. a^-1 is unique (a≠0)

7. -(-a)=a
7. -(-a)=a

8. (a^-1)^-1 =a
8. (a^-1)^-1 =a

9. a∙0=0 **Surprisingly difficult, required distributivity.
9. a∙0=0 **Surprisingly difficult, required distributivity.

10. ∄ 0^-1, aka, ∄ b∈F s.t 0∙b=1
10. ∄ 0^-1, aka, ∄ b∈F s.t 0∙b=1

11. (-a)∙(-b)=a∙b
11. (-a)∙(-b)=a∙b

Revision as of 21:57, 18 September 2012

DBN: Classes: 2012-13: 12-240 / Navigation
Additions to this web site no longer count towards good deed points.
# Week of... Notes and Links
1 Sep 10 About This Class, Tuesday, Thursday
2 Sep 17 HW1, Tuesday, Thursday, HW1 Solutions
3 Sep 24 HW2, Tuesday, Class Photo, Thursday
4 Oct 1 HW3, Tuesday, Thursday
5 Oct 8 HW4, Tuesday, Thursday
6 Oct 15 Tuesday, Thursday
7 Oct 22 HW5, Tuesday, Term Test was on Thursday. HW5 Solutions
8 Oct 29 Why LinAlg?, HW6, Tuesday, Thursday, Nov 4 is the last day to drop this class
9 Nov 5 Tuesday, Thursday
10 Nov 12 Monday-Tuesday is UofT November break, HW7, Thursday
11 Nov 19 HW8, Tuesday,Thursday
12 Nov 26 HW9, Tuesday , Thursday
13 Dec 3 Tuesday UofT Fall Semester ends Wednesday
F Dec 10 The Final Exam (time, place, style, office hours times)
Register of Good Deeds
12-240-ClassPhoto.jpg
Add your name / see who's in!
12-240-Splash.png

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

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