$x$ $+$ smaller number $=$ positive number $x$ $+$ larger number $=$ positive number $x$ $-$ smaller number $=$ positive number $x$ $-$ larger number $=$ ? However, when it comes to powers of a real number in the polynomial functions, there is an asymmetry in the result with more positive than negative results (similar to the scenario leading to negative numbers). Now I am going to use almost the same sentences in the next two lines that I used at end of the section on negative numbers: To cater for the corner case where fractional powers of $x$ are only defined for the positive half, an innovation in the form of imaginary numbers was introduced by assigning an angle as a power of $-1$ in an extra dimension to a real number.