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Simplification is the process of replacing a mathematical expression by an equivalent one that is simpler (usually shorter), according to a well-founded ordering. Examples include:
The solubility product of yttrium oxalate at 25 °C is 5.1 × 10 −30. [1] The trihydrate Y 2 (C 2 O 4) 3 •3H 2 O is formed by heating more hydrated varieties at 110 °C. [7] Y 2 (C 2 O 4) 3 •2H 2 O, which is formed by heating the decahydrate at 210 °C) forms monoclinic crystals with unit cell dimensions a=9.3811 Å, b=11.638 Å, c=5.9726 ...
In the case of two nested square roots, the following theorem completely solves the problem of denesting. [2]If a and c are rational numbers and c is not the square of a rational number, there are two rational numbers x and y such that + = if and only if is the square of a rational number d.
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]
For instance, to solve the inequality 4x < 2x + 1 ≤ 3x + 2, it is not possible to isolate x in any one part of the inequality through addition or subtraction. Instead, the inequalities must be solved independently, yielding x < 1 / 2 and x ≥ −1 respectively, which can be combined into the final solution −1 ≤ x < 1 / 2 .
For π-electron ligands such as the cyclopentadienide ion [C 5 H 5] −, alkenes and the cyclooctatetraenide ion [C 8 H 8] 2−, the number of adjacent atoms in the π-electron system that bind to the central atom is termed the hapticity. [7] In ferrocene the hapticity, η, of each cyclopentadienide anion is five, Fe(η 5-C 5 H 5) 2. Various ...
The idea becomes clearer by considering the general series 1 − 2x + 3x 2 − 4x 3 + 5x 4 − 6x 5 + &c. that arises while expanding the expression 1 ⁄ (1+x) 2, which this series is indeed equal to after we set x = 1.
In 2010 an OEIS wiki was created to simplify the collaboration of the OEIS editors and contributors. ... and the denominator sequence 5, 4, 3, 5, 2, 5, 3, 4, 5 ...