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I am trying to formally prove: $ n > \frac12 \frac xy | n \le \frac xy \lt n + 1, \forall n $

where n is an integer, and x and y are natural numbers.

It is obvious that, when $\frac xy$ is equal to n, the expression is true. I need to somehow demonstrate that, as $\frac xy$ approaches $n+1$, the expression holds true.

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    $\begingroup$ What does $\frac12 \frac xy | n$ stand for? $\endgroup$
    – BigbearZzz
    Commented Apr 3, 2016 at 2:13
  • $\begingroup$ The vertical line, or so I thought, means "such that" in formal logic. So the express is read as "n is greater than one-half multiplied by x divided by y, such that x divided by y is greater than or equal to n and less than n + 1. For all n. I might have misused the symbol "|". Please let me know if I did, and Ill correct it. $\endgroup$
    – Peter Kirby
    Commented Apr 3, 2016 at 2:15
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    $\begingroup$ It's just that the symbol "|" can be used to represent many things, and most people don't immediately relate it to formal logic's convention. I'd suggest that you rephrase it as normal English words for better understanding. $\endgroup$
    – BigbearZzz
    Commented Apr 3, 2016 at 2:21

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