is negative infinity to positive infinity the same as all real numbers
Infinity In mathematics, "infinity" is often treated as a number (i.e., it counts or measures things: "an infinite number of terms") but it is not the same sort of number as either a natural or a real number.
Real image Real images can be produced by concave mirrors and converging lenses, only if the object is placed further away from the mirror/lens than the focal point and this real image is inverted. As the object approaches the focal point the image approaches infinity, and when the object passes the focal point the image becomes virtual and is not inverted.