Is a Subset of a Countable Set also Countable?

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SUMMARY

The discussion centers on proving that a subset of a countable set is also countable. The participant emphasizes that demonstrating this general principle is more straightforward than addressing specific cases. They reference the relationship between cardinalities, specifically noting that for all natural numbers k, 2^k is not equal to 3^k, indicating the infinite nature of the set in question. This foundational concept is crucial for understanding countability in set theory.

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  • Familiarity with cardinality and its implications in mathematics.
  • Basic knowledge of natural numbers and their properties.
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Homework Statement


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I got to proof that the statement is denumberable

Homework Equations


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The Attempt at a Solution


My attempt was that 2^k != 3^k (is not) for all k in N (natural numbers)
 
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The set is obviously infinite. So now all you have to do is prove that a subset of a countable set is also countable.

I think proving this in general will be easier than attacking the specific question you posted.
 

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