MHB Finding the Maximum Value of n for a Given Equation

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The discussion revolves around finding the largest value of n for which a multiple of 4 exists between n^2 and n^2 + 2016/n^2. It is established that n^2 is less than n^2 + 2016/n^2, leading to confusion about the existence of a number that fits the criteria. Participants question the logical consistency of having a number that is both less than and greater than defined bounds. The core issue lies in reconciling the mathematical conditions set by the equation. Ultimately, the conversation highlights the complexities of the problem and the need for clarity in defining the parameters.
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What is the Largest possible value of n such that there is a multiple of 4 less than n^2 but greater than n^2 + 2016/n^2 ?
 
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I think you will agree that:

$$n^2<n^2+\frac{2016}{n^2}$$

So, how can some number be smaller than the smaller value, and at the same time greater than the greater value?
 
Meaning, there's no such thing as the smaller value, and at the same time greater than the greater value?
 

Thread 'Significant figures for inherently bound values'

I have been insisting to my statistics students that for probabilities, the rule is the number of significant figures is the number of digits past the leading zeros or leading nines. For example to give 4 significant figures for a probability: 0.000001234 and 0.99999991234 are the correct number of decimal places. That way the complementary probability can also be given to the same significant figures ( 0.999998766 and 0.00000008766 respectively). More generally if you have a value that...
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