A monitor with a HDMI input should have a resolution of at least 1920 x 1080 so that full HD images can be displayed. The number of pixels and their size determines the overall size of the monitor. To make a 19" monitor of this resolution would require smaller pixels which will increase the cost. The monitor I have has HDMI and is really 21.5" size.
Nonsense, HDMI is just a connection standard, it's got nothing to do with the content you display on the screen.
Note the word 'should' or perhaps for people like you we will all now have to preface our comments with "in my opinion".
In my opinion you should have not wasted your time with such a pointless comment when you could have provided further assistance/advice to the OP.