Two quantities are said to be different (or "unequal") if they are not equal.

The term "different" also has a technical usage related to modules. Let a module M in an integral domain D_1 for R(sqrt(D)) be expressed using a two-element basis as


where xi_1 and xi_2 are in D_1. Then the different of the module is defined as

 Delta=Delta(M)=|xi_1 xi_2; xi_1^' xi_2^'|=xi_1xi_2^'-xi_1^'xi_2.

The different Delta!=0 iff xi_1 and xi_2 are linearly independent. The module discriminant is defined as the square of the different.

See also

Equal, Module, Module Discriminant

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Cohn, H. Advanced Number Theory. New York: Dover, pp. 72-73, 1980.

Referenced on Wolfram|Alpha


Cite this as:

Weisstein, Eric W. "Different." From MathWorld--A Wolfram Web Resource.

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