[quote=Arraya]Among those omitted: part-time workers who are looking for full-time jobs and frustrated job seekers who abandon their job search altogether.[/quote]

These two groups are rightfully omitted. Part-time workers who want to work full-time are not unemployed. The argument could be made that they are under employed, but certainly not unemployed.

Finally, people who do not work and are not looking for work are, by definition, not part of the labor force. The unemployment rate would be meaningless if those in the numerator (number of unmeployed persons) are not also counted in the denominator (the labor force).