- In mathematics, the well-ordering theorem, also known as Zermelo’s theorem, states that every set can be well-ordered. A set X is well-ordered by a strict total order if every non-empty subset of X has a least element under the ordering. The well-ordering theorem together with Zorn’s lemma are the most important mathematical statements that are equivalent to the axiom of choice (often called AC, see also Axiom of choice § Equivalents). Ernst Zermelo introduced the axiom of choice as an “unobjectionable logical principle” to prove the well-ordering theorem. One can conclude from the well-ordering theorem that every set is susceptible to transfinite induction, which is considered by mathematicians to be a powerful technique. One famous consequence of the theorem is the Banach–Tarski paradox.
- September 11 attacks (Wikipedia)
The September 11 attacks, commonly known as 9/11, were four coordinated Islamist terrorist suicide attacks carried out by al-Qaeda against the United States in 2001. On that morning, 19 terrorists hijacked four commercial airliners scheduled to travel from the East Coast to California. The hijackers crashed the first two planes into the Twin Towers of the World Trade Center in New York City and aimed the next two flights toward targets in or near Washington, D.C., in an attack on the nation’s capital. The third team succeeded in striking the Pentagon, the headquarters of the U.S. Department of Defense in Arlington County, Virginia, while the fourth plane crashed in rural Pennsylvania during a passenger revolt. The September 11 attacks killed 2,977 people, making it the deadliest terrorist attack in history. In response to the attacks, the United States waged the multi-decade global war on terror to eliminate hostile groups deemed terrorist organizations, as well as the foreign governments purported to support them, in Afghanistan, Iraq, Syria, and several other countries.