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#1 2007-05-01 23:53:50

rabia
Member
Registered: 2007-05-01
Posts: 2

cardinality!

can anyone help me about what this question means and if there is a grammar error,how must be written as correctly?I think there is a grammar mistake.

   "Is the set of positive integers of smaller cardinality than the set of real numbers?"

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#2 2007-05-02 00:12:23

gnitsuk
Member
Registered: 2006-02-09
Posts: 121

Re: cardinality!

The question is asking "are there fewer positive integers than real numbers".

Basically, the cardinality of a set is its size - i.e. number of members.

So the question is asking if the number of members of the set of positive integers {1,2,3,4,...........} is less then the number of members of the set of real numbers {0.3333...,0.42424...,.........}.

The answer to this question is yes.

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#3 2007-05-02 02:19:56

rabia
Member
Registered: 2007-05-01
Posts: 2

Re: cardinality!

thanks for the answer.
  however, there is another point:is the question written correctly?I think there is a mistake.

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#4 2007-05-02 02:44:54

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: cardinality!

I don't think so. It's perhaps a bit confusing, because of all the ofs in there, but it's grammatically correct.

It might be a bit clearer if it was
"Does the set of positive integers have smaller cardinality than the set of real numbers?"

They're both asking the same question though.


Why did the vector cross the road?
It wanted to be normal.

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