<P> A dyadic relation R is symmetric if and only if, whenever it's true that Rab, it's true that Rba . Thus, "is the same age as" is symmetrical, for if Paul is the same age as Mary, then Mary is the same age as Paul . </P> <P> Symmetric binary logical connectives are and (∧, or &), or (∨, or), biconditional (if and only if) (↔), nand (not - and, or ⊼), xor (not - biconditional, or ⊻), and nor (not - or, or ⊽). </P> <P> Generalizing from geometrical symmetry in the previous section, we say that a mathematical object is symmetric with respect to a given mathematical operation, if, when applied to the object, this operation preserves some property of the object . The set of operations that preserve a given property of the object form a group . </P> <P> In general, every kind of structure in mathematics will have its own kind of symmetry . Examples include even and odd functions in calculus; the symmetric group in abstract algebra; symmetric matrices in linear algebra; and the Galois group in Galois theory . In statistics, it appears as symmetric probability distributions, and as skewness, asymmetry of distributions . </P>

Who said the world is made by symmetry and proportion