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Help with finding least upper bounds and greatest lower bounds? 
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#1
Feb2010, 11:24 PM

P: 15

1. The problem statement, all variables and given/known data
Solve the following inequalities and express the solution(s) in interval notation and set builder notation. For each of these, state the least upper bound and greatest lower bounds, if these exist. 2. Relevant equations i) x^3 + x^2 > 2x ii) l 2  x l =< 4 (modulus of 2  x is greater than or equal to 4) 3. The attempt at a solution So for (i), I factorised so x^3 + x^2  2x > 0 x(x^2 + x 2) > 0 x(x+2)(x1) > 0 I am really unsure what interval notation and set builder notation are, but I think... Interval notation: x E (2,0) U (1 , infinity) Set builder notation: {x : 2 < x < 0 or x > 1} And I don't know how to find the bounds... (ii) l 2  x l =< 4 4 =< 2  x =< 4 6 =< x =< 2 interval notation: x E [2,6] set builder notation: {x: 2 =< x =< 6} and... i don't know how to find the least upper bounds/greatest lower bounds for this either. =/ 


#2
Feb2110, 01:43 AM

Mentor
P: 21,280

For the interval (1, infinity), there is no upper bound, so there isn't a least upper bound. The greatest lower bound is 1, which is not an element of this interval. 


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