HDR Photos contain all the light present in a scene. This can be considerably more light than you can capture in a single exposure, and certainly much more than a regular monitor can display.
So, what is a Real HDR image?
Is it an image where all the light is truthfully represented? Even if that means your monitor can only show a slice of it? Or is it an image, where you can see the full dynamic range at once? Then I have to compress that range for you, using tonemapping. And how far can that go and still be considered truthful?