A microprocessor is a device capable of automatically carrying out a sequence of operations on data expressed in discrete (digital) or continuous (analog) form. The purpose of a computer or a microprocessor is to solve a problem or class of problems; the problem may be one of control, analysis, or a combination of the two. Without a doubt, any problem a computer can solve, a man could solve. The advantage is one of time. On a series of complex analytical problems, a mathematician could dedicate his entire life to doing what a computer could do in mere seconds; similarly, no human could continuously analyze new stimuli and generate responses in the microsecond intervals required by modern electronics and electromechanical hardware.
As much as we fefer to computers for microprocessors as one entity, we will try to spell out capability, structure, and economic differences.