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find infimum A=(-2,3]

Guest May 25, 2014

Best Answer 

 #2
avatar+80933 
+5

I don't know much about this, but the way I understand it is that the infimum of a set of numbers is the largest number that is less than or equal to all the numbers in the set.
The supremum of a set of numbers is the smallest number that is greater than or equal to all the numbers in the set. 

Also, as I understand it, the infimum of a set doesn't actually have to belong to the set itself. Based on this, -2 should be your answer, because it's the largest number that is less than or equal to all the members of (-2, 3]. Notice that it doesn't belong to the set itself.

If someone on the forum knows more about this, I'll stand corrected......

CPhill  May 26, 2014
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 #1
avatar+91436 
0

I am not sure what your question is. However:

The round bracket means the -2 is not actually included and the square bracket means that it is included.

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$$-2

Melody  May 25, 2014
 #2
avatar+80933 
+5
Best Answer

I don't know much about this, but the way I understand it is that the infimum of a set of numbers is the largest number that is less than or equal to all the numbers in the set.
The supremum of a set of numbers is the smallest number that is greater than or equal to all the numbers in the set. 

Also, as I understand it, the infimum of a set doesn't actually have to belong to the set itself. Based on this, -2 should be your answer, because it's the largest number that is less than or equal to all the members of (-2, 3]. Notice that it doesn't belong to the set itself.

If someone on the forum knows more about this, I'll stand corrected......

CPhill  May 26, 2014
 #3
avatar+91436 
0

Thanks Chris, I had never heard of that term before!

Melody  May 26, 2014

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