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  2. Comparability - Wikipedia

    en.wikipedia.org/wiki/Comparability

    Hasse diagram of the natural numbers, partially ordered by "x≤y if x divides y".The numbers 4 and 6 are incomparable, since neither divides the other. In mathematics, two elements x and y of a set P are said to be comparable with respect to a binary relation ≤ if at least one of x ≤ y or y ≤ x is true.

  3. Turing's proof - Wikipedia

    en.wikipedia.org/wiki/Turing's_proof

    Any number N (in base 8) can be converted to an S.D with the following replacements: 1 by A, 2 by C, 3 by D, 4 by L, 5 by R, 6 by N, 7 by semicolon ";". As it turns out, machine H's unique number (D.N) is the number "K". We can infer that K is some hugely long number, maybe tens-of-thousands of digits long. But this is not important to what ...

  4. Proof of impossibility - Wikipedia

    en.wikipedia.org/wiki/Proof_of_impossibility

    Another consequential proof of impossibility was Ferdinand von Lindemann's proof in 1882, which showed that the problem of squaring the circle cannot be solved [2] because the number π is transcendental (i.e., non-algebraic), and that only a subset of the algebraic numbers can be constructed by compass and straightedge.

  5. Computational complexity of mathematical operations - Wikipedia

    en.wikipedia.org/wiki/Computational_complexity...

    Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations.

  6. Congruence relation - Wikipedia

    en.wikipedia.org/wiki/Congruence_relation

    In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector space) that is compatible with the structure in the sense that algebraic operations done with equivalent elements will yield equivalent elements. [1]

  7. Compatibility (mechanics) - Wikipedia

    en.wikipedia.org/wiki/Compatibility_(mechanics)

    The problem of compatibility in continuum mechanics involves the determination of allowable single-valued continuous fields on simply connected bodies. More precisely, the problem may be stated in the following manner. [5] Figure 1. Motion of a continuum body. Consider the deformation of a body shown in Figure 1.

  8. Can you solve this math problem meant for 14-year-olds?

    www.aol.com/news/2015-04-14-can-you-solve-this...

    HARTFORD, Conn. (FOXCT) - Standardized testing in the United States has been quite a controversial topic in recent years. Some argue schools are putting too much focus on mastering the test, than ...

  9. Pell number - Wikipedia

    en.wikipedia.org/wiki/Pell_number

    In words: the first two numbers in the sequence are both 2, and each successive number is formed by adding twice the previous Pell–Lucas number to the Pell–Lucas number before that, or equivalently, by adding the next Pell number to the previous Pell number: thus, 82 is the companion to 29, and 82 = 2 × 34 + 14 = 70 + 12.