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.

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 forms of the game, association croquet and golf croquet, have rules that are agreed internationally and are played in many countries around the world.

The rules of Set are summarized by: If you can sort a group of three cards into " Two of ____ and one of _____ ," then it is not a set.

* David Manley-author of " Iron and Fire ", " Fox Two " and other air and naval rules systems, editor of the Naval Wargames Society journal " Battlefleet "

At the end of Part One ( concentrating on the history ), it was announced that Part Two ( about the rules ) had been postponed due to " scheduling difficulties ".

Two books of rules and history have been published, The Little Book of Mornington Crescent ( 2001 ; ISBN 0-7528-1864-3 ), by Graeme Garden, Tim Brooke-Taylor, Barry Cryer and Humphrey Lyttelton, and Stovold's Mornington Crescent Almanac ( 2001 ; ISBN 0-7528-4815-1 ), by Graeme Garden.

Two of these guiding principals were and still are ; " No surcharges should be imposed on payments in cash "; and " Member States should not adopt new rounding rules to the nearest five cent ".

* Two Australian rules footballers:

Two to eight players is common, though eight may require special rules for the last cards dealt if no players fold.

Two statements of the same basic rules, differing only in wording, are given here.

Thereafter the race was run to Formula Two rules until 1985, and thereafter by its replacement, Formula 3000.

Two of these " rules " included a prohibition on hanging laundry out to dry on Sunday and not allowing homeowners to fence off their yards.

Two fans, however, revised Myranor to be played with the " final " 4th edition rules with FanPro's permission.

Two leagues have played under the official arena football rules: the AFL, which played 22 seasons from 1987 to 2008 and resumed play under new ownership in 2010, and arenafootball2, the AFL's erstwhile developmental league, which played 10 seasons from 2000 through 2009.

Two units of 15mm spearmen from a Phocis ( ancient region ) | Phokian Greek army under De Bellis Antiquitatis rules. Scale is generally expressed as the approximate height of a humanoid figure from base of foot to eyeline ( though some count to top of head – hence the possible confusion ) in millimeters, this is sometimes referred to as the Barret Scale, as opposed to the ratio values used in scale modeling.

However, there was a non-Championship German Grand Prix run to Formula Two rules at the Nürburgring that year, that was won by Alberto Ascari in a Ferrari.

It last published its rules in the 1950s ; the National Two Ball Roque Association last published its revised rules in 1961.

Two elements and of the free group on a set are conjugate if and only if, when they are written as products of elements and with in, and then those products are put in cyclic order, the cyclic orders are equivalent under the rewriting rules that allow one to remove or add adjacent and.

Two corollary rules of the doctrine, the personal attack rule and the " political editorial " rule, remained in practice until 2000.

# Kil ' ayim ( כלאים, Of Two Sorts ; Heterogeneous ) deals chiefly with rules regarding forbidden mixtures in agriculture, clothing and breeding ( Leviticus 19: 19 ; Deuteronomy 22: 9 – 11 ).

Two are most noteworthy: the banning of punting, meaning that if a team felt it was not likely to get a first down after three plays its only kicking option was to attempt a field goal, even if it were of the very unlikely distance of 60 yards or more ( Foster had also instituted rules that had favored the drop kick as a substitute for the punt, but such rules were rarely used ); and the placing of rebound nets around the ends of the playing surface.

Two rules are used, cutting and creasing rules.