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  2. Projectile motion - Wikipedia

    en.wikipedia.org/wiki/Projectile_motion

    In projectile motion, the horizontal motion and the vertical motion are independent of each other; that is, neither motion affects the other. This is the principle of compound motion established by Galileo in 1638, [ 1 ] and used by him to prove the parabolic form of projectile motion.

  3. Law of trichotomy - Wikipedia

    en.wikipedia.org/wiki/Law_of_trichotomy

    A law of trichotomy on some set X of numbers usually expresses that some tacitly given ordering relation on X is a trichotomous one. An example is the law "For arbitrary real numbers x and y, exactly one of x < y, y < x, or x = y applies"; some authors even fix y to be zero, [1] relying on the real number's additive linearly ordered group structure.

  4. Module (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Module_(mathematics)

    An (R,S)-bimodule is an abelian group together with both a left scalar multiplication · by elements of R and a right scalar multiplication ∗ by elements of S, making it simultaneously a left R-module and a right S-module, satisfying the additional condition (r · x) ∗ s = r ⋅ (x ∗ s) for all r in R, x in M, and s in S.

  5. Four fours - Wikipedia

    en.wikipedia.org/wiki/Four_fours

    For example, when d=4, the hash table for two occurrences of d would contain the key-value pair 8 and 4+4, and the one for three occurrences, the key-value pair 2 and (4+4)/4 (strings shown in bold). The task is then reduced to recursively computing these hash tables for increasing n , starting from n=1 and continuing up to e.g. n=4.

  6. Kepler's laws of planetary motion - Wikipedia

    en.wikipedia.org/wiki/Kepler's_laws_of_planetary...

    The orbits are ellipses, with foci F 1 and F 2 for Planet 1, and F 1 and F 3 for Planet 2. The Sun is at F 1. The shaded areas A 1 and A 2 are equal, and are swept out in equal times by Planet 1's orbit. The ratio of Planet 1's orbit time to Planet 2's is (/) /.

  7. Simple module - Wikipedia

    en.wikipedia.org/wiki/Simple_module

    Z-modules are the same as abelian groups, so a simple Z-module is an abelian group which has no non-zero proper subgroups.These are the cyclic groups of prime order.. If I is a right ideal of R, then I is simple as a right module if and only if I is a minimal non-zero right ideal: If M is a non-zero proper submodule of I, then it is also a right ideal, so I is not minimal.

  8. Proof by infinite descent - Wikipedia

    en.wikipedia.org/wiki/Proof_by_infinite_descent

    In mathematics, a proof by infinite descent, also known as Fermat's method of descent, is a particular kind of proof by contradiction [1] used to show that a statement cannot possibly hold for any number, by showing that if the statement were to hold for a number, then the same would be true for a smaller number, leading to an infinite descent and ultimately a contradiction. [2]

  9. Cyclic module - Wikipedia

    en.wikipedia.org/wiki/Cyclic_module

    2Z as a Z-module is a cyclic module. In fact, every cyclic group is a cyclic Z-module. Every simple R-module M is a cyclic module since the submodule generated by any non-zero element x of M is necessarily the whole module M. In general, a module is simple if and only if it is nonzero and is generated by each of its nonzero elements. [2]

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