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Israel security cabinet approves plan to expand Gaza offensive newsthirst.

Israel’s security cabinet has approved a plan to expand its military offensive against Hamas, which reportedly includes capturing Gaza and holding the territory. The Israeli military has called up tens of thousands of reservists in preparation for the move, saying it is “increasing the pressure” with the aim of bringing home the remaining Israeli hostages…

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Israel says it will expand its offensive across most of Gaza newsthirst.

Israel’s defence minister has announced the military will soon “expand vigorously” its offensive throughout most of Gaza. Israel Katz also said the Israel Defense Forces (IDF) had completed the takeover of a “security zone” in the southern part of the Gaza Strip, separating the cities of Rafah and Khan Younis. Israel’s military also issued evacuation…

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New Proofs Expand the Limits of What Cannot Be Known newsthirst.

In other words, Hilbert’s 10th problem is undecidable. Mathematicians hoped to follow the same approach to prove the extended, rings-of-integers version of the problem—but they hit a snag. Gumming Up the Works The useful correspondence between Turing machines and Diophantine equations falls apart when the equations are allowed to have non-integer solutions. For instance, consider…

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