The term selectivity (S) is used to describe the relative rates of two or more competing reactions on a catalyst. Such competition includes cases of different reactants undergoing simultaneous reactions or of a single reactant taking part in two or more reactions. For the latter case, S may be defined in two ways. The first of these defines a fractional selectivity, S F, for each product by the equation \[S_{\text{F}}=\frac{\xi _{i}}{\sum \xi _{i}}\] The second defines relative selectivities, S R, for each pair of products by \[S_{\text{R}}=\frac{\xi _{i}}{\xi _{j}}\] In each case, ξ i and ξ j are the rates of increase of the extent of reactions i and j respectively, i.e. \[\xi _{i}=\frac{\mathrm{d}\xi _{i}}{\mathrm{d}t}\] and \[\xi _{j}=\frac{\mathrm{d}\xi _{j}}{\mathrm{d}t}\] where ξ i and ξ j are the extents of reactions i and j respectively.