** Assume that the initial peg is on the left and the final peg is on the right.

** Tarski's theorem: For every infinite set A, there is a bijective map between the sets A and A × A.

** For every non-empty set S there is a binary operation defined on S that makes it a group.

** If the set A is infinite, then there exists an injection from the natural numbers N to A ( see Dedekind infinite ).

** The Vitali theorem on the existence of non-measurable sets which states that there is a subset of the real numbers that is not Lebesgue measurable.

** On every infinite-dimensional topological vector space there is a discontinuous linear map.

** for all f in X ′ there exists x in X with ǁxǁ ≤ 1, so that f ( x ) = ǁfǁ.

** Structural mapping: the locations of the major rock units and the faults and folds that led to their placement there.

** At Sint-Pieters-Station and the Zuid bus station there are several regional buses as well.

** Elizabeth of Portugal, patron saint of Coimbra ( city holiday ), known there as Rainha Santa Isabela.

** Quasi-realism, defended by Simon Blackburn, holds that ethical statements behave linguistically like factual claims and can be appropriately called " true " or " false ", even though there are no ethical facts for them to correspond to.

** Amongst them, there are those who hold that moral knowledge is gained inferentially on the basis of some sort of non-moral epistemic process, as opposed to ethical intuitionism.

** Although the original 68000 CPU was designed by Motorola, there are many clones of this CPU found in the Neo Geo hardware.

** 1 in Mogadishu, the Radio Mogadishu the Government Owned radio station, also there is private Radio who transmit Mainly on Shortwaves like Shabelle and Mustaqbal Radio owned by Mustaqbal Media corporation ( MMC )

** Bare assertions – making entirely unsubstantiated claims-may also be considered a form of research misconduct although there is no evidence that cases of this form have ever led to a finding of misconduct.

** the act of appointing ( i. e. giving ) an asset from the trust to a beneficiary ( usually where there is some choice in the matter — such as in a discretionary trust ); or

** In the Tajik Soviet Socialist Republic, rioting breaks out against the settlement of Armenian refugees there.

** Swede Göran Kropp reaches the Mount Everest summit alone without oxygen, after having bicycled there from Sweden.

** In San Francisco, during his second televised debate with Jimmy Carter, U. S. President Gerald Ford stumbles when he declares that " there is no Soviet domination of Eastern Europe " ( there is at the time ).

** King Mahendra of Nepal deposes the democratic government there and he takes direct control himself.

** Vietnam War: White House Press Secretary Ron Ziegler tells the press that there will be no more public announcements concerning United States troop withdrawals from Vietnam due to the fact that troop levels are now down to 27, 000.

** The World War I Allies demand that the Netherlands extradite the German Kaiser Wilhelm II, who has fled there.

** A guard takes his place at the Tomb of the Unknowns in Washington, DC ; continuous guard has been maintained there ever since.

** Vietnam War – Operation Ivory Coast: A joint Air Force and Army team raids the Son Tay prison camp in an attempt to free American POWs thought to be held there ( no Americans are killed, but the prisoners have already moved to another camp ; all U. S. POWs are moved to a handful of central prison complexes as a result of this raid ).

** China Airlines Flight 006 is involved in a mid-air incident ; while there are twenty two minor injuries and two serious injuries, no one is killed.

** Trichotomy: If two sets are given, then either they have the same cardinality, or one has a smaller cardinality than the other.

** The additive groups of R and C are isomorphic.

** The numbers and are algebraic since they are roots of polynomials and, respectively.

** The numbers and are not algebraic numbers ( see the Lindemann – Weierstrass theorem ); hence they are transcendental.

** In topology, morphisms between topological spaces are called continuous maps, and an automorphism of a topological space is a homeomorphism of the space to itself, or self-homeomorphism ( see homeomorphism group ).

** Congenital adrenal hyperplasias are genetic defects of enzymes involved in cortisol production and can affect sex characteristics of affected patients.

** Through initiatory experiences whereby the reality of Christ's death and resurrection are experienced ; Steiner believed this is the path people will increasingly take.

** howitzers: capable of high angle fire, they are most often employed for indirect-fire.

** Speed: 1. 79 MHz, drops to 1. 19 MHz when the TIA Television Interface Adaptor or RIOT ( 6532 RAM-I / O-Timer ) chips are accessed

** Nine of his centuries are double centuries ( surpassed only by Donald Bradman )

** Two of them are triple-centuries ( matched by Australia's Donald Bradman, India's Virender Sehwag, and West Indies ' Chris Gayle ).

** β-Lactams containing thiazolidine rings are named penams.

** β-Lactams containing pyrrolidine rings are named carbapenams.

** β-Lactams fused to oxazolidine rings are named oxapenams or clavams.

** β-Lactams containing 2, 3-dihydrothiazole rings are named penems.

** β-Lactams containing 2, 3-dihydro-1H-pyrrole rings are named carbapenems.

** β-Lactams containing 3, 6-dihydro-2H-1, 3-thiazine rings are named cephems.

** β-Lactams containing 1, 2, 3, 4-tetrahydropyridine rings are named carbacephems.

** β-Lactams containing 3, 6-dihydro-2H-1, 3-oxazine rings are named oxacephems.

** A more apocalyptic passage comparing the locusts to an army, and revealing that they are God ’ s army.

** The Nintendo DS and the Nintendo DS Lite are backward compatible with all Game Boy Advance games.

** Initial PlayStation 3 models are backward compatible with most PlayStation and PlayStation 2 games.

** Between Basel SBB and Basel Badischer Bahnhof – Basel Badischer Bahnhof, and all other railway property and stations on the right bank of the Rhine belong to DB and are classed as German customs territory.