I'm trying to prove that if given the innumerable set A and the set B = {x, y}, then A X B is denumerable as well. Proof: All I have so far is that, assuming A is denumerable, we can create the sequence A = a1, a2, a3, ... By definition of cross-product, we can then form the sequence A X B = a1x, a1y, a2x, a2y, a3x, a3y, ...It should be clear that this sequence includes every element of AXB as, as such, A X B is denumerable. I am not entirely sure that this argument is valid.

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Answered: A and the set B = {x, y}, then A X B is…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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I'm trying to prove that if given the innumerable set A and the set B = {x, y}, then A X B is denumerable as well.

Proof:

All I have so far is that, assuming A is denumerable, we can create the sequence A = a₁, a₂, a₃, ... By definition of cross-product, we can then form the sequence A X B = a₁x, a₁y_, a₂x, a₂y, a₃x, a₃y, ...

It should be clear that this sequence includes every element of AXB as, as such, A X B is denumerable.

I am not entirely sure that this argument is valid.

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