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The word "class" in the term "equivalence class" may generally be considered as a synonym of "set", although some equivalence classes are not sets but proper classes. For example, "being isomorphic" is an equivalence relation on groups, and the equivalence classes, called isomorphism classes, are not sets.
For example, sulfuric acid (H 2 SO 4) is a diprotic acid. Since only 0.5 mol of H 2 SO 4 are needed to neutralize 1 mol of OH −, the equivalence factor is: f eq (H 2 SO 4) = 0.5. If the concentration of a sulfuric acid solution is c(H 2 SO 4) = 1 mol/L, then its normality is 2 N. It can also be called a "2 normal" solution.
The row and column indices of nonwhite cells are the related elements, while the different colors, other than light gray, indicate the equivalence classes (each light gray cell is its own equivalence class). In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive.
It can be easily shown that conjugacy is an equivalence relation and therefore partitions into equivalence classes. (This means that every element of the group belongs to precisely one conjugacy class, and the classes Cl ( a ) {\displaystyle \operatorname {Cl} (a)} and Cl ( b ) {\displaystyle \operatorname {Cl} (b)} are equal if and ...
The solution has 1 mole or 1 equiv Na +, 1 mole or 2 equiv Ca 2+, and 3 mole or 3 equiv Cl −. An earlier definition, used especially for chemical elements , holds that an equivalent is the amount of a substance that will react with 1 g (0.035 oz) of hydrogen , 8 g (0.28 oz) of oxygen , or 35.5 g (1.25 oz) of chlorine —or that will displace ...
Canonical forms are generally used to make operating with equivalence classes more effective. For example, in modular arithmetic, the canonical form for a residue class is usually taken as the least non-negative integer in it. Operations on classes are carried out by combining these representatives, and then reducing the result to its least non ...
The Brauer group plays an important role in the modern formulation of class field theory. If K v is a non-Archimedean local field, local class field theory gives a canonical isomorphism inv v : Br K v → Q/Z, the Hasse invariant. [2] The case of a global field K (such as a number field) is addressed by global class field theory.
Equivalence classes (sets of elements such that x R y and y R x) are shown together as a single node. The relation on equivalence classes is a partial order. In mathematics, especially in order theory, a preorder or quasiorder is a binary relation that is reflexive and transitive.