System of inequalities - proving n = kLet's say we have the following inequalities: n &lt; x + 1 ≤ k + 1and k &lt; x + 1 ≤ n + 1How to prove that n = k?

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System of inequalities - proving   n  =  kLet&#039;s say we have the following inequalities:  n  &amp;lt;  x  +  1  ≤  k  +  1and  k  &amp;lt;  x  +  1  ≤  n  +  1How to prove that   n  =  k?

SuefsSeeltHeRn8 · Accepted Answer

The statements  n  &amp;lt;  x  +  1  ≤  k  +  1and  k  &amp;lt;  x  +  1  ≤  n  +  1mean   n  &amp;lt;  x  +  1 and   x  +  1  ≤  k  +  1 and   k  &amp;lt;  x  +  1 and   x  +  1  ≤  n  +  1.So we have  n  &amp;lt;  x  +  1  ≤  n  +  1and  k  &amp;lt;  x  +  1  ≤  k  +  1.That is, the largest integer less than   x  +  1 is   n and that same integer is   k. Therefore   n  =  k.

vittorecostao1 · Accepted Answer

From the inequalities you can deduce that  k  &amp;lt;  x  +  1  ≤  k  +  1  n  &amp;lt;  x  +  1  ≤  n  +  1Since each set of   N has exactly one minimun you can conclude that   n  =  k because   n and   k are two number satisfying a minimun propierty.

System of inequalities - proving n = k Let's say we have the following inequalities:

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