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October 21st, 2011, 01:08 AM  #1 
Newbie Joined: Oct 2011 Posts: 16 Thanks: 0  Help with notation I've never seen Hi all, I was wondering whether you could help with an issue I have. Basically I have no idea what any of this means. I was given these exercises and I don't even know where to start. So is the set of {0,1,2,...,j1}? So I know that j and p are elements of the natural numbers (a) so does this mean that the cardinality of set j is equal to some element (b) I have no idea here? what is it asking (c) again no idea So my questions, What does the underline mean? And can someone help me work through each of the exercises above? As you have probably worked out I am new to discrete maths and set theory so any help would be much obliged. Thanks Dina 
October 21st, 2011, 05:15 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Help with notation I've never seen
a asks if the cardinality of {0, 1, 2, ..., j1} is j. b asks if the cardinality of {0} plus the cardinality of {0} is the cardinality of {0, 1}. etc. 
October 21st, 2011, 05:23 AM  #3 
Senior Member Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0  Re: Help with notation I've never seen
b) doesn't appear to be about the cardinality of the sets; I am unsure as to whether S+T in this context refers to union of S and T or the set (although in this case it's the same thing). is the set 
October 21st, 2011, 05:25 AM  #4 
Newbie Joined: Oct 2011 Posts: 16 Thanks: 0  Re: Help with notation I've never seen
Hi thanks, so is this right? (a) True  cardinality of is going to be a natural number (b) True  Cardinality of + is the cardinality of (c) Not to sure on this one. How would I show this? I get the impression it's false, but that's just from intuition. 
October 21st, 2011, 05:38 AM  #5  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Help with notation I've never seen
Sorry  as mattpi points out, b doesn't use cardinality symbols. I'm not sure what + is supposed to mean; what does your book have for it? Quote:
For c, do you understand what it is saying?  
October 21st, 2011, 06:19 AM  #6 
Newbie Joined: Oct 2011 Posts: 16 Thanks: 0  Re: Help with notation I've never seen
My book doesn't state anything for '+' or at least not what I can see. I am now really confused. So (a) isn't true? surely the cardinality of is the natural number j, or does it not mean this. And for (c) I have no idea what it means. Perhaps give me an example. This is really confusing me, thanks for all the help and your time and trouble Dina 
October 21st, 2011, 06:29 AM  #7  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Help with notation I've never seen Quote:
Once you understand a, c becomes easy.  
October 21st, 2011, 06:38 AM  #8 
Newbie Joined: Oct 2011 Posts: 16 Thanks: 0  Re: Help with notation I've never seen
Ok I really don't understand (a). Surely the cardinality of any set is a natural number. Lets assume that we're including 0 in the set of natural numbers, in which case surely (a) is always true? Could you explain (a) in more detail to me? I'm sorry for being such an idiot but this is really confusing me. Thanks Dina 
October 21st, 2011, 07:02 AM  #9  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Help with notation I've never seen Quote:
But that's not what the problem asks! It's asking if , not if Do you see the difference?  
October 21st, 2011, 07:14 AM  #10 
Newbie Joined: Oct 2011 Posts: 16 Thanks: 0  Re: Help with notation I've never seen
Ok I do see the difference, in that case (a) is true since is equal to j, if j is 1 for example then and it's cardinality is 1, not just any arbitrary natural number. Is that correct? Thanks Dina 

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