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The notation R^_ denotes the set of affinely extended real numbers.

A measure that takes on real values.

A quadratic field Q(sqrt(D)) with D>0.

A relation R on a set S is reflexive provided that xRx for every x in S.

A reflexive relation.

The least positive integer m^* with the property that chi(y)=1 whenever y=1 (mod m^*) and (y,m)=1.

Euclidean n-space is denoted R^n.

A position in a game is safe for a player A if the person who plays next (player B) will lose.

The modular equation of degree five can be written (u/v)^3+(v/u)^3=2(u^2v^2-1/(u^2v^2)).

A property of finite simple groups which is known for all such groups.