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What will be the supremum and infimum of the set { m/(|m|+n) : n- natural numbers, m- integers}?
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(Original post by Infinity ∞)
What will be the supremum and infimum of the set { m/(|m|+n) : n- natural numbers, m- integers}?
What will be the supremum and infimum of the set { m/(|m|+n) : n- natural numbers, m- integers}?
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Think about how n changes the expression m/(|m|+n). Try varying it to extremes.
It's really helpful in these problems when one of the numbers changes the expression monotonically. Is the function f(n) = m/(|m|+n) monotonic over the natural numbers? This helps us to find the extreme values. Notice though that this will be different depending on whether m is positive or negative.
It's really helpful in these problems when one of the numbers changes the expression monotonically. Is the function f(n) = m/(|m|+n) monotonic over the natural numbers? This helps us to find the extreme values. Notice though that this will be different depending on whether m is positive or negative.
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(Original post by Infinity ∞)
What will be the supremum and infimum of the set { m/(|m|+n) : n- natural numbers, m- integers}?
What will be the supremum and infimum of the set { m/(|m|+n) : n- natural numbers, m- integers}?
Try vary m and n looking at extremal cases. You should be able to check your answer over at Wolframalpha.com/
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