Difference between revisions of "09-240/Classnotes for Tuesday September 15"
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# <math>a + b = c + d \Rightarrow a = c </math> "cancellation property" | # <math>a + b = c + d \Rightarrow a = c </math> "cancellation property" | ||
# <math> a \cdot b = c \cdot b , (b \ne 0) \Rightarrow a = c </math> | # <math> a \cdot b = c \cdot b , (b \ne 0) \Rightarrow a = c </math> | ||
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Revision as of 21:25, 15 September 2009
File:Classnotes For Tuesday, September 15.jpg yangjiay:09-240 Classnotes for Tuesday September 15 2009 page 5.jpg
The real numbers A set with two binary operators and two special elements s.t.
- Note: or means inclusive or in math.
Definition: A field is a set F with two binary operators : F×F → F, : F×F → F and two elements s.t.
Examples
-
- is not a field (counterexample)
Theorem: for is a field IFF is a prime number
Tedious Theorem
- "cancellation property"
...