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2. Collatz conjecture - Wikipedia

   en.wikipedia.org/wiki/Collatz_conjecture

   For instance, the first counterexample must be odd because f(2n) = n, smaller than 2n; and it must be 3 mod 4 because f 2 (4n + 1) = 3n + 1, smaller than 4n + 1. For each starting value a which is not a counterexample to the Collatz conjecture, there is a k for which such an inequality holds, so checking the Collatz conjecture for one starting ...

3. Elementary algebra - Wikipedia

   en.wikipedia.org/wiki/Elementary_algebra

   The graph of the logarithm to base 2 crosses the x axis (horizontal axis) at 1 and passes through the points with coordinates (2, 1), (4, 2), and (8, 3). For example, log 2 (8) = 3, because 2 3 = 8. The graph gets arbitrarily close to the y axis, but does not meet or intersect it.

4. Algebraic expression - Wikipedia

   en.wikipedia.org/wiki/Algebraic_expression

   Since taking the square root is the same as raising to the power ⁠ 1 / 2 ⁠, the following is also an algebraic expression: 1 − x 2 1 + x 2 {\displaystyle {\sqrt {\frac {1-x^{2}}{1+x^{2}}}}} An algebraic equation is an equation involving polynomials , for which algebraic expressions may be solutions .

5. Debris falls from roof at home of Cowboys before game against ...

   www.aol.com/debris-falls-roof-home-cowboys...

   The roof hasn't been opened for a Cowboys game in their $1.2 billion stadium since the 2022 season. “I know we opened it long before any fans or anybody is in there,” owner Jerry Jones said ...

6. Elementary arithmetic - Wikipedia

   en.wikipedia.org/wiki/Elementary_arithmetic

   Elementary arithmetic is a branch of mathematics involving addition, subtraction, multiplication, and division. Due to its low level of abstraction, broad range of application, and position as the foundation of all mathematics, elementary arithmetic is generally the first branch of mathematics taught in schools. [1] [2]

7. Russia arrests suspected cartel members, seizes $55 million ...

   www.aol.com/russia-arrests-suspected-cartel...

   Russia said Friday it had arrested suspected members of a Colombian cartel trying to smuggle tens of millions of dollars worth of cocaine into Europe.. The suspects were caught loading 570 ...