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  2. 30 Math Puzzles (with Answers) to Test Your Smarts - AOL

    www.aol.com/30-math-puzzles-answers-test...

    Answer: 6. Read from left to right as a series of numbers that are always divided by four (or by two if you alternate between the top and bottom rows). 96 ÷ 4 = 24; 24 ÷ 4 = 6 (or 06); 48 ÷ 4 = 12.

  3. Negative number - Wikipedia

    en.wikipedia.org/wiki/Negative_number

    This thermometer is indicating a negative Fahrenheit temperature (−4 °F). In mathematics, a negative number is the opposite of a positive real number. [1] Equivalently, a negative number is a real number that is less than zero. Negative numbers are often used to represent the magnitude of a loss or deficiency.

  4. Negation - Wikipedia

    en.wikipedia.org/wiki/Negation

    As a further example, negation can be defined in terms of NAND and can also be defined in terms of NOR. Algebraically, classical negation corresponds to complementation in a Boolean algebra, and intuitionistic negation to pseudocomplementation in a Heyting algebra. These algebras provide a semantics for classical and intuitionistic logic.

  5. Integer - Wikipedia

    en.wikipedia.org/wiki/Integer

    For example Leonhard Euler in his 1765 Elements of Algebra defined integers to include both positive and negative numbers. [ 15 ] The phrase the set of the integers was not used before the end of the 19th century, when Georg Cantor introduced the concept of infinite sets and set theory .

  6. Proof of impossibility - Wikipedia

    en.wikipedia.org/wiki/Proof_of_impossibility

    In mathematics, an impossibility theorem is a theorem that demonstrates a problem or general set of problems cannot be solved. These are also known as proofs of impossibility, negative proofs, or negative results. Impossibility theorems often resolve decades or centuries of work spent looking for a solution by proving there is no solution.

  7. Rule of replacement - Wikipedia

    en.wikipedia.org/wiki/Rule_of_replacement

    In logic, a rule of replacement [1] [2] [3] is a transformation rule that may be applied to only a particular segment of an expression.A logical system may be constructed so that it uses either axioms, rules of inference, or both as transformation rules for logical expressions in the system.

  8. Proof by contradiction - Wikipedia

    en.wikipedia.org/wiki/Proof_by_contradiction

    Its negation ¬H(M) states that "M neither halts nor does not halt", which is false by the law of noncontradiction (which is intuitionistically valid). If proof by contradiction were intuitionistically valid, we would obtain an algorithm for deciding whether an arbitrary Turing machine M halts, thereby violating the (intuitionistically valid ...

  9. Negation normal form - Wikipedia

    en.wikipedia.org/wiki/Negation_normal_form

    Negation normal form is not a canonical form: for example, () and () are equivalent, and are both in negation normal form. In classical logic and many modal logics , every formula can be brought into this form by replacing implications and equivalences by their definitions, using De Morgan's laws to push negation inwards, and eliminating double ...

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