Names for the number 0 in English the score was not placed upon a scoreboard, and there is scant evidence that the French ever used "l'oeuf" as the name for a zero score in the first place, that name being as anecdotal as the hypothesis that "love" is then derived from it. (Jacob Bernoulli, for example, in his "Letter to a Friend", used "à but" to describe the initial zero–zero score in court tennis, which in English is "love-all".) Some alternative hypotheses have similar problems. For example: The assertion that "love" comes from the Scots word "luff", meaning "nothing", falls at the first hurdle, because there is
Zero of a function a "zero locus". In analysis and geometry, any closed subset of formula_32 is the zero set of a smooth function defined on all of formula_32. This extends to any smooth manifold as a corollary of paracompactness. In differential geometry, zero sets are frequently used to define manifolds. An important special case is the case that formula_1 is a smooth function from formula_35 to formula_32. If zero is a regular value of formula_1, then the zero set of formula_1 is a smooth manifold of dimension formula_39 by the regular value theorem. For example, the unit formula_40-sphere in formula_41 is the zero