12-240/Classnotes for Thursday September 13: Difference between revisions
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'''F1:''' commutative law |
'''F1:''' commutative law |
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<math>\forall \!\,</math> a, b <math>\in \!\,</math> F: a+b=b+a and a.b=b.a |
<math>\forall \!\,</math> a, b <math>\in \!\,</math> F: a+b=b+a and a.b=b.a |
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'''F2:''' associative law |
'''F2:''' associative law |
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<math>\forall \!\,</math> a, b, c <math>\in \!\,</math> F: (a+b)+c=a+(b+c) |
<math>\forall \!\,</math> a, b, c <math>\in \!\,</math> F: (a+b)+c=a+(b+c) |
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Revision as of 16:34, 13 September 2012
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In the second day of the class, the professor continues on the definition of a field.
Definition of a field
Combined with a part from the first class, we have a complete definition as follow:
A field is a set "F' with two binary operations +,x defind on it, and two special elements 0 ≠ 1 such that
F1: commutative law
a, b F: a+b=b+a and a.b=b.a
F2: associative law
a, b, c F: (a+b)+c=a+(b+c)
