Difference between revisions of "06-240/Classnotes For Tuesday, September 12"

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=Notes=
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==The Real Numbers==
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The Real Numbers are a set (denoted by <math>\mathbb{R}</math>) along with two binary operations: + (plus) and &middot; (times) and two special elements: 0 (zero) and 1 (one), such that the following laws hold true: <p>
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<math>\mathbb{R}1 :\forall a, b\in \mathbb{R} \quad a\cdot b=b\cdot a \quad \mbox{and} \quad a+b=b+a</math> (The Commutative Laws)

Revision as of 22:46, 22 September 2006

  • 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
  • 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 \mathbb{R}) along with two binary operations: + (plus) and · (times) and two special elements: 0 (zero) and 1 (one), such that the following laws hold true:

\mathbb{R}1 :\forall a, b\in \mathbb{R} \quad a\cdot b=b\cdot a \quad \mbox{and} \quad a+b=b+a (The Commutative Laws)