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Problems 1–6 compute divisions of a certain number of loaves of bread by 10 men and record the outcome in unit fractions. Problems 7–20 show how to multiply the expressions 1 + 1/2 + 1/4 = 7/4, and 1 + 2/3 + 1/3 = 2 by different fractions. Problems 21–23 are problems in completion, which in modern notation are simply subtraction problems ...
Between November 1938 and April 1941, Hungary took full advantage of German patronage and, in four different stages, approximately doubled her size. Ethnically, these acquisitions were a mixed bag, some were populated mostly by Hungarians, while others, such as the remainder of Carpathian Ruthenia, were almost wholly non-Hungarian in composition.
That month, Vienna was divided into ... +0.7%: 2011: 1,714,227 +10.6%: ... The population of Vienna generally stagnated or declined through the remainder of the 20th ...
Engraving of Fra Paolo Sarpi by George Vertue (1684–1756) Paolo Sarpi, Calcografia Bettoni, Milan, 1824. Paolo Sarpi (14 August 1552 – 15 January 1623) was a Venetian historian, prelate, scientist, canon lawyer, polymath and statesman active on behalf of the Venetian Republic during the period of its successful defiance of the papal interdict (1605–1607) and its war (1615–1617) with ...
A series or, redundantly, an infinite series, is an infinite sum.It is often represented as [8] [15] [16] + + + + + +, where the terms are the members of a sequence of numbers, functions, or anything else that can be added.
The least ordinal of cardinality ℵ 0 (that is, the initial ordinal of ℵ 0) is ω but many well-ordered sets with cardinal number ℵ 0 have an ordinal number greater than ω. For finite well-ordered sets, there is a one-to-one correspondence between ordinal and cardinal numbers; therefore they can both be expressed by the same natural ...
The sum turned out to be so large (£3,000,000) that it prompted the First Opium War, [267] The 1842 Treaty of Nanking – the beginning of the unequal treaties that restricted Qing sovereignty in the 19th century – is generally taken to have ended China's isolation, with the opening of the ports of Xiamen ("Amoy"), Fuzhou ("Fuchow"), Ningbo ...