- #1
Mr Davis 97
- 1,462
- 44
If I write ##-1 \le\cos x \le 1##, we all clearly know what this means, that not only is ##\cos x## contained in this interval but that its max is 1 and its min is -1. However, what if I write ##-1 \le \cos n \le 1##, where ##n \in \mathbb{N}##. What does the inequality mean in this case? This inequality is still true, but it doesn't say anything about the max or the min. I guess my question is this, in what cases can we suppose that an inequality is saying something about a max or a min, and in what cases is the inequality simply stating that something is bounded above or below?