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 sets have the same cardinal number if and only if there is a bijection 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 early 20th century writers and their debt to the poet.

Two extremely controversial undertakings by the county account for the majority of this debt.

Two factions grew up around the issue of debt relief.

Two years later, plagued by debt, Santōka ’ s younger brother Jirō committed suicide.

He claims a thematic debt, for both Fistful and Yojimbo, to Carlo Goldoni's Servant of Two Masters — the basic premise of the protagonist playing two camps off against each other.

Two of its proponents stated: " By implementing a fair tax code, by building a resilient American economy, and by bringing our troops home, we achieve a budget surplus of over $ 30 billion by 2021 and we end up with a debt that is less than 65 % of our GDP.

Two phenomena allowed Martin to reshape the magazine and bring it back from the abyss of debt.

His early works, such as Two Gongs ( 1971 ) owed a significant debt to Young and other minimalists.

Two years previously the company had been declared bankrupt and receivers appointed ; it was unable to pay the charges on its debt.

Two years later, on 1 August, it was forced to relegate to Tercera División after not being able to pay a debt of € 700, 000 euros, which consequently led to the club being dissolved.

Two of the holders exchanged their Albert Medals for the George Cross in 1971.

Two days after the letters were sent, YRC announced it had obtained the necessary thresholds on its bond holder debt-to-equity exchange offer, which was the final part of a comprehensive restructuring plan that required all major stakeholders — its workers, pension funds, secured lenders and bond holders — to contribute toward helping the company survive the worst freight recession in generations.

Two ships of the Royal Navy have borne the name HMS Duke of York, after numerous holders of the title of Duke of York:

Two prominent gas holders, which are used to store the consumer gas supply for south west London stand just south of the shopping parade and can be seen from a wide area.

Two of the participants ( holders ) face each other about 3 feet apart, with their feet together, and position the rope around their ankles so that it is taut.

Two idiot mechanics ( fruit and veg / fish stall holders in the later series ) commenting on current affairs much in the same mode as " Pete and Dud ".

Two of the participants ( the " holders ") will hold the rope taut at increasing heights ( e. g. ankle, knee, hip, usually ending with the holders ' arms in the air ), while the third participant ( the " jumper ") must jump over the rope.