SOLUTION: Consider the finite number of sets A1= (−1,1), A2= [1,10), A3= [−10,−1], A4= [10,∞), and A5= (−∞,−10). Prove or disprove that there is a partitionof real numbers for
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Question 1167127: Consider the finite number of sets A1= (−1,1), A2= [1,10), A3= [−10,−1], A4= [10,∞), and A5= (−∞,−10). Prove or disprove that there is a partitionof real numbers for the collection {A1, A2, A3, A4, A5}.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
The five sets together exactly cover the whole number line without overlap, so they form a partition of the real numbers.
A5: -infinity to -10, not including -10
A3: -10 to -1, including both endpoints
A1: -1 to 1, including neither endpoint
A2: 1 to 10, including 1 but not 10
A4: 10 to infinity, including 10
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