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 Katie C. 04-26-2013 11:33 AM

meaning of union of hypothesis sets

I am trying to understand the union of hypothesis sets. Do we get hypotheses that were not in any of the original hypothesis sets? For example, if we take H1 to be the set of positive intervals on the real line, and H2 to be the set of 2 positive intervals (that we saw in HW3 Q6) on the real line, in the union do we have hypotheses with 3 positive intervals?

 yaser 04-26-2013 11:42 AM

Re: meaning of union of hypothesis sets

Quote:
 Originally Posted by Katie C. (Post 10609) I am trying to understand the union of hypothesis sets. Do we get hypotheses that were not in any of the original hypothesis sets? For example, if we take H1 to be the set of positive intervals on the real line, and H2 to be the set of 2 positive intervals (that we saw in HW3 Q6) on the real line, in the union do we have hypotheses with 3 positive intervals?
You get only hypotheses that were in one set or the other, but no added "combinations." It follows the formal definition of a union of sets (hypothesis sets or any other type of sets); the union being the set of all elements that appear in any of those sets (and nothing else).

 binchen.bin@gmail.com 04-26-2013 01:48 PM

Re: meaning of union of hypothesis sets

So by definition the union of hypothesis sets does not give rise to any new hypothesis, but the intersection of hypothesis sets may eliminate some hypothesis. Is that right?

 yaser 04-26-2013 02:41 PM

Re: meaning of union of hypothesis sets

Quote:
 Originally Posted by binchen.bin@gmail.com (Post 10611) So by definition the union of hypothesis sets does not give rise to any new hypothesis, but the intersection of hypothesis sets may eliminate some hypothesis. Is that right?
Correct.

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