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This article analyzes the print culture of the Black and multiethnic community known as L8 in the northern British city of Liverpool. Through a critique of printed materials, including newsletters, magazines, and pamphlets all written, produced and read within the locale, the author assesses the construction of a community that was at once imagined and lived. This print infrastructure facilitated a collective sense of L8 as a marker of identity and belonging in a city and a nation that otherwise often harbored racialized hostility to the residents’ economic and political interests. Such a commitment to the locale, the author asserts, became a key factor in organizing the collective action taken by the residents in the 1981 Toxteth protests. Before and after that event, the neighborhood's print culture served to justify to residents the reasons for taking violent action against the state. Equally, this source material highlights the fissures and divergences between neighbors in their deliberations over the definitions—and limitations—of such a community and its relation to the nation. The author thus offers new ways to think about Black British protest in close relation to the specific political and social dynamics of neighborhoods across Britain.
A number of deep theorems and unsolved problems ask questions about the relationship of the additive and multiplicative structure of the natural numbers. The famous four squares theorem of Lagrange says that if we form all possible sums of four squares we get the entire sequence of nonnegative integers. Goldbach’s conjecture states that if all possible sums of two odd primes are formed we get every even integer greater than 4.
The depth and difficulty of such problems stand in surprising contrast to the similar question: “Which numbers are not generated when all possible sums of two or more consecutive natural numbers are formed?” The answer is all powers of 2 and the proof is accessible to anyone who can sum arithmetic sequences. This result is an excellent discovery exercise for students, particularly appropriate for teacher training courses.
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