Department of Mathematics
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Here, 'nothing' is a metaphor for the trivial variety consisting of just one-element groups defined by the equation "x=y", while the phrase 'much ado' corresponds to the infinitely many equational descriptions of the trivial variety by independent symmetrical equational bases (of arbitrarily large size). In fact we prove that the trivial variety has an independent symmetric basis with n identities for all n>1 . This is a generalization of a well-known result of Alfred Tarski on the cardinalities of irredundant equational bases. A similar statement is also true for irredundant presentations of the trivial group in terms of generators and relations.

(*) with due apologies to William Shakespeare