
#1
Feb1313, 04:44 AM

P: 376

##S = \bigcup _{i=1}^{∞}\left\{{0,1}\right\}^i ##
methinks yes because: ##S = \bigcup _{i=1}^{∞}\left\{{0,1}\right\}^i \equiv \left\{{0,1}\right\}^\mathbb{N}## 



#2
Feb1313, 05:07 AM

Mentor
P: 16,591





#3
Feb1313, 06:12 AM

P: 376





#4
Feb1313, 07:33 AM

Mentor
P: 16,591

Is this set uncountable 



#5
Feb1313, 12:38 PM

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#6
Feb1313, 02:37 PM

P: 90

I think that [itex]S = \bigcup _{i=1}^{∞}\left\{{0,1}\right\}^i[/itex] is countable all right. The mapping with [itex]\mathbb{N}[/itex] is quite obvious.




#7
Feb1313, 10:46 PM

P: 376

Thanks guys, yes it is kind of clear that ## \bigcup_{i=1}^{∞}\left\{{0,1}\right\}^i ## is countable...I was just looking too much into it.
I believe my confusion was coming from misunderstanding the set: ##\left\{{0,1}\right\}^\mathbb{N}## which has the cardinality of the power set of ##\mathbb{N}##. 


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