Difference between revisions of "06-240/Classnotes For Tuesday, September 12"
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* PDF notes by [[User:Harbansb]]: [[Media:06-240-0912.pdf|September 12 Notes]]. | * PDF notes by [[User:Harbansb]]: [[Media:06-240-0912.pdf|September 12 Notes]]. | ||
* If I have made an error in my notes, or you would like the editable OpenOffice file, feel free to e-mail me at harbansb@msn.com. | * If I have made an error in my notes, or you would like the editable OpenOffice file, feel free to e-mail me at harbansb@msn.com. | ||
− | * [http://www.yousendit.com/transfer.php?action=download | + | * [http://www.yousendit.com/transfer.php?action=download&ufid=38FF36BF7ED1E1BA September 12 Notes] for re-uploading, please email at jeff.matskin@utoronto.ca |
+ | * PDF notes by [[User:Alla]]: [[Media:MAT_Lect001.pdf|Week 1 Lecture 1 notes]] | ||
+ | * Below are a couple of lemmata critical to the derivation we did in class - the Professor left this little work to the students: | ||
+ | ::[[Image:Edit1.jpg|200px]] [[Image:Edit2.jpg|200px]] | ||
+ | |||
+ | =Notes= | ||
+ | |||
+ | ==The Real Numbers== | ||
+ | The Real Numbers are a set (denoted by <math>\mathbb{R}</math>) along with two binary operations: + (plus) and · (times) and two special elements: 0 (zero) and 1 (one), such that the following laws hold true: | ||
+ | |||
+ | <math>\mathbb{R}1</math>: <math>\forall a, b\in \mathbb{R}</math> we have <math>a+b=b+a</math> and <math>a\cdot b=b\cdot a</math> (The Commutative Laws) | ||
+ | |||
+ | <math>\mathbb{R}2</math>: <math>\forall a, b, c\in \mathbb{R}</math> we have <math>(a+b)+c=a+(b+c)</math> and <math>(a\cdot b)\cdot c=a\cdot (b\cdot c)</math> (The Associative Laws) | ||
+ | |||
+ | <math>\mathbb{R}3</math>: <math>0</math> is an additive unit and <math>1</math> is a multiplicative unit (The Existence of Units/Identities) | ||
+ | |||
+ | <math>\mathbb{R}4</math>: <math>\forall a\in \mathbb{R} \ \exists b\in \mathbb{R} \mbox{ s.t.} \ a+b=0</math> | ||
+ | |||
+ | This is incomplete. |
Latest revision as of 18:13, 11 July 2007
|
- PDF notes by User:Harbansb: September 12 Notes.
- If I have made an error in my notes, or you would like the editable OpenOffice file, feel free to e-mail me at harbansb@msn.com.
- September 12 Notes for re-uploading, please email at jeff.matskin@utoronto.ca
- PDF notes by User:Alla: Week 1 Lecture 1 notes
- Below are a couple of lemmata critical to the derivation we did in class - the Professor left this little work to the students:
Notes
The Real Numbers
The Real Numbers are a set (denoted by ) along with two binary operations: + (plus) and · (times) and two special elements: 0 (zero) and 1 (one), such that the following laws hold true:
: we have and (The Commutative Laws)
: we have and (The Associative Laws)
: is an additive unit and is a multiplicative unit (The Existence of Units/Identities)
:
This is incomplete.