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Define the two measures on the real line as = [,] () = [,] for all Borel sets. Then and are equivalent, since all sets outside of [,] have and measure zero, and a set inside [,] is a -null set or a -null set exactly when it is a null set with respect to Lebesgue measure.
An equivalent (symbol: officially equiv; [1] unofficially but often Eq [2]) is the amount of a substance that reacts with (or is equivalent to) an arbitrary amount (typically one mole) of another substance in a given chemical reaction. It is an archaic quantity that was used in chemistry and the biological sciences (see Equivalent weight § In ...
The titer corresponds to the highest dilution factor that still yields a positive reading. [2] For example, positive readings in the first 8 serial, twofold dilutions translate into a titer of 1:256 (i.e., 2 −8). Titres are sometimes expressed by the denominator only, for example 1:256 is written 256. [3]
An equivalent formulation of the ideal gas law can be written using Boltzmann constant k B, as P V = N k B T , {\displaystyle PV=Nk_{\text{B}}T,} where N is the number of particles in the gas, and the ratio of R over k B is equal to the Avogadro constant .
2 1.8 Rational Functions and Zeros 1 1.9 Rational Functions and Vertical Asymptotes 1 1.10 Rational Functions and Holes 1 1.11 Equivalent Representations of Polynomial and Rational Expressions 2 1.12 Transformations of Functions 2 1.13 Function Model Selection and Assumption Articulation 2 1.14 Function Model Construction and Application 2
In mathematics, the method of equating the coefficients is a way of solving a functional equation of two expressions such as polynomials for a number of unknown parameters. It relies on the fact that two expressions are identical precisely when corresponding coefficients are equal for each different type of term.
An algebraic equation is an equation involving polynomials, for which algebraic expressions may be solutions. If you restrict your set of constants to be numbers, any algebraic expression can be called an arithmetic expression. However, algebraic expressions can be used on more abstract objects such as in Abstract algebra.
That is, in grams, the atomic weight of the element divided by the usual valence. [2] For example, the equivalent weight of oxygen is 16.0/2 = 8.0 grams. For acid–base reactions, the equivalent weight of an acid or base is the mass which supplies or reacts with one mole of hydrogen cations (H +).
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