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Proof Must Have
. Statement of what is to be proven.
. "Proof:" to indicate where the proof starts
. Clear indication of flow
. Clear indication of reason for each step
. Careful notation, completeness and order
. Clear indication of the conclusion
. I suggest pencil and good erasure when needed
Number Theory  Ch 3 Definitions
. Z  integers
. Q  rational numbers (quotients of integers)
r?Q ??a,b?Z, (r = a/b) ^ (b ? 0)
. Irrational = not rational
. R  real numbers
. superscript of
+
 positive portion only
. superscript of

 negative portion only
. other superscripts: Z
even
, Z
odd
, Q
>5
. "closure" of these sets for an operation
 Z closed under what operations?
Integer Definitions
. even integer
n ?Z
even
??k ? Z, n = 2k
. odd integer
n ? Z
odd
??k ? Z, n = 2k+1
. prime integer (Z
>1
)
n ?Z
prime
??r,s?Z
+
, (n=r*s) ?(r=1)v(s=1)
. composite integer (Z
>1
)
n ? Z
composite
??r,s?Z
+
, n=r*s ^(r?1)^(s?1)
Constructive...
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