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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. Mathematical visualization - Wikipedia

    en.wikipedia.org/wiki/Mathematical_visualization

    The Mandelbrot set, one of the most famous examples of mathematical visualization.. Mathematical phenomena can be understood and explored via visualization.Classically, this consisted of two-dimensional drawings or building three-dimensional models (particularly plaster models in the 19th and early 20th century).

  4. Multiple representations (mathematics education) - Wikipedia

    en.wikipedia.org/wiki/Multiple_representations...

    The use of multiple representations supports and requires tasks that involve decision-making and other problem-solving skills. [2] [3] [4] The choice of which representation to use, the task of making representations given other representations, and the understanding of how changes in one representation affect others are examples of such mathematically sophisticated activities.

  5. System of linear equations - Wikipedia

    en.wikipedia.org/wiki/System_of_linear_equations

    The solution set for the equations x − y = −1 and 3x + y = 9 is the single point (2, 3). A solution of a linear system is an assignment of values to the variables ,, …, such that each of the equations is satisfied. The set of all possible solutions is called the solution set. [5]

  6. Division by two - Wikipedia

    en.wikipedia.org/wiki/Division_by_two

    An orange that has been sliced into two halves. In mathematics, division by two or halving has also been called mediation or dimidiation. [1] The treatment of this as a different operation from multiplication and division by other numbers goes back to the ancient Egyptians, whose multiplication algorithm used division by two as one of its fundamental steps. [2]

  7. George Stubbs dog painting expected to sell for up to $2.5 ...

    www.aol.com/george-stubbs-dog-painting-expected...

    A painting by British artist George Stubbs is expected to sell for up to £2 million ($2.5 million) in London next week, as it comes to auction for the first time in more than 50 years.. The 18th ...

  8. New Jersey internet gambling sets another revenue record at ...

    www.aol.com/jersey-internet-gambling-sets...

    A dealer conducts a card game at the Hard Rock casino in Atlantic City, N.J., on Oct. 3, 2024, a month in which internet gambling set a new revenue record in New Jersey at $213 million.

  9. Elon Musk calls for 'deleting' the Consumer Financial ... - AOL

    www.aol.com/finance/elon-musk-calls-deleting...

    November 27, 2024 at 4:34 PM. Billionaire Elon Musk, a key adviser to the incoming Trump administration, called for the Consumer Financial Protection Bureau to be eliminated, setting his sights on ...