Two sets A and B are defined to be equal when they have precisely the same elements, that is, if every element of A is an element of B and every element of B is an element of A.

Two sets are said to have the same cardinality or cardinal number if there exists a bijection ( a one-to-one correspondence ) between them.

Two such functions are deemed equivalent when their respective sets of fixpoints have the same cardinality, corresponding to cycles of length one in a permutation.

* 1860 – Giuseppe Garibaldi sets sail from Genoa, leading the expedition of the Thousand to conquer the Kingdom of the Two Sicilies and giving birth to the Kingdom of Italy.

Two or three sound stages and four outdoor sets were destroyed ; fortunately, the rest of the Studios were still intact.

The centerpiece of the deregulation was the establishment of two categories of basic services licenses: Local loop ( LL ), for fixed line telecommunication within the 14 PTCL regions, and Long-distance and International ( LDI ), for connectivity between regions .” Two sets of criteria set by the regulatory authorities must be met before an operator is allowed to start operation: one for the issuance of a license and another for the maintenance of service quality.

Two blocks with a rope attached to one of the blocks and threaded through the two sets of pulleys form a block and tackle.

Two sets of rules exist, each of which can be played with a variety of layouts.

The Deep Cameo versions of proofs from 1965 to 1971 and 1981 Type Two are highly valued because of their scarcity, high grade examples of quarters from certain years of the 1980s ( such as 1981 – 1987 ) because of scarcity in high grades due to high circulation and in 1982 and 1983 no mint sets were produced making it harder to find mint state examples, and any coin from 1981 – 1994 graded in MS67 is worth upwards of $ 1000.

* Bruce Quarrie-wrote rule sets for Napoleonic and World War Two wargames and also on military history.

Two 1-connected paths can be consolidated together if the two groups of stones they start and end in are the same and their empty-point sets do not overlap.

Two sets of accents are spoken in the West Country, Cornish ( primarily in South Cornwall ) and West Country ( the counties of Devon, Somerset, Gloucestershire, Bristol, Dorset ( Not so much in east Dorset ), Wiltshire ( again, less so in eastern Wiltshire ), and also in East Cornwall ).

Two sets of 6 attitude control nitrogen jets were mounted on the ends of the solar panels.

Two disjoint sets.

Two sets are called similar if one is the image of the other under such a similarity.

Two other sets of units, Gaussian and CGS-EMU, are the same for magnetic properties and are commonly used in physics.

The third, " Coursing between the Two Poles ", involves three sets of movements which aim to enable the expulsion of bad energy ( e. g. pathogenic or black qi ) and the absorption of good energy into the body.

Two sets of extremists had arisen: Northerners who demanded no new slave territories under any circumstances, and Southerners who demanded free entry for slavery into all territories, the penalty for denial to be secession.

Two different sets of numbers bear this name: the Stirling numbers of the first kind and the Stirling numbers of the second kind.

Two forces converged to initiate the PDB: 1 ) a small but growing collection of sets of protein structure data determined by X-ray diffraction ; and 2 ) the newly available ( 1968 ) molecular graphics display, the Brookhaven RAster Display ( BRAD ), to visualize these protein structures in 3-D.

Two sets of brothers, Jacob and Daniel Beck and George and Daniel Miller first stopped in Williamsport before moving further to the north.

Battle Kings reappeared on the market in 2006, but not as King Size models, but rather as a name of military-oriented Two Pack-style sets of regular size models.

Two sets of death duties in the 1940s, and the nationalization of their coal mines, greatly reduced the wealth of the Fitzwilliams, and most of the contents of the house were dispersed, in auction sales in 1948, 1986 and 1998, though many remain in the family, with many works loaned to museums by the " Trustees of the Fitzwilliam Estates ".

Two sets of pronunciations for the numerals exist in Japanese: one is based on Sino-Japanese ( on ' yomi ) readings of the Chinese characters and the other is based on the Japanese yamato kotoba ( native words, kun ' yomi readings ).

Two facets of this aspect of the literary process have special significance for our time.

Two things have happened in recent months to bring the Council into perspective: each provides a basis for renewed hope and joy.

Two data centers have been established for the collection, indexing, critical evaluation, and dissemination of bibliographies and critical values in the fields of transition probabilities and collision cross sections.

Two stories will illustrate what I have in mind.

Two days before he was taken sick, Cousin Elec was out worrying about what too much rain might do to his sweetpeas, and Cousin Elec had always preserved in the top drawer of his secretary a mother-of-pearl paper knife which Theresa had coveted as a child and which he had promised she could have when he died.

Two related strands of research on altruism have emerged from traditional evolutionary analyses and from game theory.

Two works by Mauss in particular proved to have enduring relevance: Essay on the Gift, a seminal analysis of exchange and reciprocity, and his Huxley lecture on the notion of the person, the first comparative study of notions of person and selfhood cross-culturally.

Two other groups have similar inflorescences but a superior ovary, and have at times been put into separate families: the Agapanthaceae and the Alliaceae.

Two small sanctuaries, with terracotta votive offerings of Graeco-Phoenician age, lie not far off, but the location of the great shrines of Adonis and Aphrodite have not been identified ( M. Ohnefalsch-Richter, Kypros, i. ch. 1 ).

Two points in this brief description have attracted much scholarly commentary.

Two of Ammonius's students-Origen the Pagan, and Longinus-seem to have held philosophical positions which were closer to Middle Platonism than Neoplatonism, which perhaps suggests that Ammonius's doctrines were also closer to those of Middle Platonism than the Neoplatonism developed by Plotinus ( see the Enneads ), but Plotinus does not seem to have thought that he was departing in any significant way from that of his master.

Two other genera, Echinosphaerium and Camptonema, have been described but appear to be synonyms.

Two, from the Venus tablet of Ammisaduqa ( compiled in Babylon around 1700 BCE ) are reported to have been made during the reign of king Sargon of Akkad ( 2334 – 2279 BCE ).

Two theories of the direct initiation of apoptotic mechanisms in mammals have been suggested: the TNF-induced ( tumour necrosis factor ) model and the Fas-Fas ligand-mediated model, both involving receptors of the TNF receptor ( TNFR ) family coupled to extrinsic signals.

Two spiritual adversaries endeavour to tempt and corrupt humanity: these are often described through their mythological embodiments, Lucifer and his counterpart Ahriman, which have both positive and negative aspects.

Two Aegean vases were found at Sidon in 1885, and many fragments of Aegean and especially Cypriot pottery have been found during recent excavations of sites in Philistia by the Palestine Fund.

How do you do ?," Capp sardonically congratulated Lennon and Ono on their Two Virgins nude album cover: " I think that everybody owes it to the world to prove they have pubic hair.

The characters have made cameo appearances ( either visually or only voices ) and have been referenced in numerous television shows, such as Friends, Two and a Half Men, Celebrity Deathmatch, Robot Chicken, Space Ghost Coast to Coast, and Saturday Night Live ( TV Funhouse ), in films such as Airheads, Clueless, Austin Powers: International Man of Mystery and Jackass 3D, and even parodied in children shows such as Tiny Toon Adventures, Regular Show and Arthur.

Two groups of invertebrates have notably complex brains: arthropods ( insects, crustaceans, arachnids, and others ), and cephalopods ( octopuses, squids, and similar molluscs ).< ref name = Butler > The brains of arthropods and cephalopods arise from twin parallel nerve cords that extend through the body of the animal.

Two investigations have been held by the British government.

Two centuries ago, mummies were still believed to have medicinal properties against bleeding, and were sold as pharmaceuticals in powdered form ( see human mummy confection and mummia ).