Since the book is intended to be self-contained, all necessary results of set theory, topology, measure theory, descriptive set theory are revisited with the purpose to eliminate superfluous use of an axiom of choice.
Superfluous design elements are anathema to Apple.
Of the two hundred and twelve members of the Legislature, two hundred and ten are, for all intents and purposes, superfluous, like so many extras from "Gangs of New York".
This modest attempt would grant Frege's point that negative judgements are superfluous for the purposes of logic, while at the same time accepting Brentano's view that, when it comes to the classification of mental phenomena, negative judgments play a fundamental role.
In retrospect, the projection of U.S power and influence was superfluous and had no purpose.
It is, notably, a legal requirement that has stayed in place until this day, although completely superfluous, and could have no purpose other than to insult those who are unable to marry but wish to.
We cannot adequately defend ourselves against further attacks unless we, like the terrorists, maintain an unyielding sense of purpose, one uninfluenced by superfluous issues.
Living light eliminates the superfluous and reframes mindsets that reflect purpose.
Because re-designing an existing tool proved costly, a for the purpose of this study superfluous feature, (the Likert scales), was left unchanged, and this may have unavoidably influenced the results, for instance those relating to time investment.
In order to avoid superfluous criteria, Bolzano stated only the most concrete purpose in his definition, for the other tasks are entailed by it.
