When my teacher was teaching us and operator inequalities she gave us a problem as homework in which the question boiled down to 4.5≤q<4.5 so next day she got to the question and said it was infinite solutions but on my paper I had no solutions so I called her out on it and she said that it was indeed all solutions and that there are special circumstances in which it's like this, so I started to fiddle with the problem and I indeed found it No Solutions. Am I right to believe this or am I being a dunce? If I'm right how do I tell her?