Hint: Use the fundamental theorem of arithmetic. 15. Theorem 14.5 implies that Nx N is countably infinite. Construct an alternate proof of this fact by showing that the function ф : N x N 2n-1(...

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15. Theorem 14.5 implies that Nx N is countably infinite. Construct an alternate proof of this fact by showing that the funct
Hint: Use the fundamental theorem of arithmetic.

It is also true that the Cartesian product of two countably infinite sets is itself countably infinite, as our next theorem s

15. Theorem 14.5 implies that Nx N is countably infinite. Construct an alternate proof of this fact by showing that the function ф : N x N 2n-1(2m-1) is bijective. N defined as ф(m,n)
It is also true that the Cartesian product of two countably infinite sets is itself countably infinite, as our next theorem states. Theorem 14.5 If A and B are both countably infinite, then so is A x B. Proof. Suppose A and B are both countably infinite. By Theorem 14.3, we know we can write A and B in list form as }, A = 例,a2,a3,a4,

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Hint: Use the fundamental theorem of arithmetic. 15. Theorem 14.5 implies that Nx N is countably infinite. Construct an alternate proof of this fact by showing that the function ф : N x N 2n-1(...

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Hint: Use the fundamental theorem of arithmetic. 15. Theorem 14.5 implies that Nx N is countably infinite. Construct an alternate proof of this fact by showing that the function ф : N x N 2n-1(...

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Hint: Use the fundamental theorem of arithmetic. 15. Theorem 14.5 implies that Nx N is countably infinite. Construct an alternate proof of this fact by showing that the function ф : N x N 2n-1(...

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Add Answer to: Hint: Use the fundamental theorem of arithmetic. 15. Theorem 14.5 implies that Nx N is countably infinite. Construct an alternate proof of this fact by showing that the function ф : N x N 2n-1(...

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Hint: Use the fundamental theorem of arithmetic. 15. Theorem 14.5 implies that Nx N is countably infinite. Construct an alternate proof of this fact by showing that the function ф : N x N 2n-1(...