Recall, a rule assigning elements of a set A to a set B is said to...
Recall, a rule assigning elements of a set A to a set B is said to be well-defined if the assignment of elements in A to those of B is unique. Furthermore, such a rule is said to be a function when it is well-defined. Consider the rule f : Q → Z where f m n = m − n for any q = m n ∈ Q. Explain why this rule is not a function.
Homework Answers
Note that the m/n representation of a specific rational number is not unique. That is,
and so on.
Thus in this case 
and again
.
Hence this rule is not well-defined. Hence f is not a function.
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Recall, a rule assigning elements of a set A to a set B is said
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problem 23 please :) and here is Q.21 Problem 23. Recall from Problem 21 the equivalence...
problem 23 please :)
and here is Q.21
Problem 23. Recall from Problem 21 the equivalence relation ~ on the set of rational Cauchy sequences C. Define 〈z) E C to be eventually positive if there is an M є N such that xn > 0 for all Prove that eventually positive is a well defined notion on c/ (z〉 ~ 〈y), then 〈y〉 İs eventually positive. ie. if 〈z) is eventually positive and Problem 21. Let C be the...
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Let U be a set, and let A CU. Recall the indicator function XA: U +...
Let U be a set, and let A CU. Recall the indicator function XA: U + Z, defined by XA(x) = ſi, rEA 0, A. Now, let A, B CU and consider the symmetric difference of A and B defined by A AB= (A - B)U(B - A). (a) Show that AAB CU, and compute Ø A A. (b) Prove that Ve EU, XAAB(C) = XA(2) + XB(2), where addition is taken modulo 2 (so that 1+1 = 0).
1. (9pts) Suppose A is a set with m elements and B is a set with...
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(2) For an integer n, let Z/nZ denote the set of equivalence classes [k) tez: k -é is divisible by n (a) Prove that the set Z/nZ has n elements. (b) Find a minimal set of representatives for these n elements. (c) Prove that the operation gives a well-defined addition on Z/nZ Hint: The operution should not depend on the choice of coset representatives Verify that this gives Z/n2 the structure of an ahelian group. Be sure to verify all...
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problem 23 please :)
and here is Q.21
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