Counting infinite sequence of sets

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Homework Help Overview

The discussion revolves around the concept of countability in set theory, specifically focusing on an infinite sequence of countable sets and the properties of their union.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants express confusion about the definition of countable sets and the implications of bijections. Questions arise regarding the notation used, such as "ZZ+" and "NxN," and their meanings in the context of countability.

Discussion Status

The discussion is currently exploratory, with participants seeking clarification on foundational concepts. Some guidance has been offered regarding the definitions of countability and bijections, but there is no consensus on the understanding of the notation or the initial problem.

Contextual Notes

Participants are grappling with the terminology and notation related to countability, which may be impacting their ability to engage with the problem effectively.

ihatewonders
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Let K1, K2, K3, . . . be an infnite sequence of sets, where each set Kn is countable.
Prove that the union of all of these sets K = Union from n=1 to infinity, Kn is countable.

I tried to start, but I don't even understand the question

Need some idea on how to start
 
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Not understanding the question is not a good start. What does 'countable' mean?
 
Denumerable?

The set K would be denumberable if there is a bijection ZZ+->K

by the way, can you teach me how to read "Bijection ZZ+->K?" ZZ+ is the symbol for all positive integer, -> is the arrow pointing to the set K.
and I have trouble understanding what F: NN -> A mean intuitively
 
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I don't know what you are talking about. What does ZZ+->X mean? Countable means there is a bijection with N, the natural numbers. This is basically the same proof as showing NxN is countable. How do you do that?
 
I'm sorry, >.< but what does NxN mean? is it the symbol for natural number?
 

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