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math239-26052008

Section 1(c sloss math 239 introduction to binary

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Unformatted text preview: Section 1 (C. Sloss) MATH 239: May 26, 2008 Introduction to Binary Strings Unique generation Motivation Definitions 4. Operations on Binary Strings Let a = a 1 ··· a n and b = b 1 ··· b m be binary strings. The concatenation of a and b is the binary string ab := a 1 ··· a n b 1 ··· b m . Let A , B be sets of binary strings. The concatenation product of A and B is AB := { ab : a ∈ A , b ∈ B } Recall that the cartesian product of two sets is A × B := { ( a , b ) : a ∈ A , b ∈ B } . Example : Let A = { , 01 , 11 } and B = { 1 , 11 } . Section 1 (C. Sloss) MATH 239: May 26, 2008 Introduction to Binary Strings Unique generation 5. Definition of Unique Generation Definition : If | A × B | = | AB | , then we say AB is uniquely generated. Example : A = { , 01 , 11 } and B = { , 11 } . If AB is uniquely generated, then Φ AB ( x ) = Φ A ( x )Φ B ( x ) . AB is uniquely generated if and only if “delete commas and parentheses” is a bijection from A × B to AB ....
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Section 1(C Sloss MATH 239 Introduction to Binary Strings...

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