Suppose I have $0 < N - \varepsilon < q$ where $N$ is some large real number and $\varepsilon$ is much smaller than $N$. Can I conclude that $0 < N - \varepsilon < N < q$?
Determining when an inequality holds
-1
$\begingroup$
elementary-number-theory
-
0Please accept any useful answers that you have received. You could see [How do I accept an answer?](http://meta.math.stackexchange.com/questions/3286/how-do-i-accept-an-answer) – 2012-09-17
-
0@RossMillikan: when someone has only asked 5 questions, I don't think it's *that* unlikely none of the answers are acceptable... – 2012-09-17
2 Answers
2
No. You have $0
-
0Thanks. Is there a theorem which tells us when something like this is true? – 2012-09-17
-
0Trivially, it is true whenever $q>N+\epsilon$, or equivalently whenever $q-N>\epsilon$. I'm really not sure what you're going for here... – 2012-09-17
-
0I was wondering if given these arbitrary quantities, we can somehow deduce the second inequality. – 2012-09-17
-
0I'm not sure why you would think that. – 2012-09-17
-
0Never mind. Thanks. – 2012-09-17
2
Think about $0 < 100000 - 2 < 99999$ ...