An identity function ''f'' is a function (mathematics) which does not have any effect: it always returns the same value that was used as its argument. Formally, if ''M'' is a set, the identity function id''M'' on ''M'' is defined to be that function with domain (mathematics) and codomain ''M'' which satisfies :id''M''(''x'') = ''x'' for all elements ''x'' in ''M''. If ''f'' : ''M'' → ''N'' is any function, then we have ''f'' o id''M'' = ''f'' = id''N'' o ''f'' (where "o" denotes function composition). In particular, id''M'' is the identity element of the monoid of all functions from ''M'' to ''M''. When choosing ''M'' equal to the positive integers, one obtains the identity function Id(''n''), which is a multiplicative function considered in number theory. Elementary_mathematics
I changed back to the previous version for the following reasons: * The identity function is in general not multiplicative. Only in the special case of ''M'' = positive integers could it be called a multiplicative function. But there are many other sets ''M'' out there. * We don't use colors in formulas * Blackboard bold is reserved for sets of numbers, like R or C. Letters that stand for functions, sets or variables are normally written in italic. user:AxelBoldt, Thursday, April 18, 2002
See other meanings of words starting from letter:
Words begining with Identity_function:
Identity_function
Identity_function
Identity function
An identity function ''f'' is a function (mathematics) which does not have any effect: it always returns the same value that was used as its argument. Formally, if ''M'' is a set, the identity function id''M'' on ''M'' is defined to be that function with domain (mathematics) and codomain ''M'' which satisfies :id''M''(''x'') = ''x'' for all elements ''x'' in ''M''. If ''f'' : ''M'' → ''N'' is any function, then we have ''f'' o id''M'' = ''f'' = id''N'' o ''f'' (where "o" denotes function composition). In particular, id''M'' is the identity element of the monoid of all functions from ''M'' to ''M''. When choosing ''M'' equal to the positive integers, one obtains the identity function Id(''n''), which is a multiplicative function considered in number theory. Elementary_mathematics
Identity function
I changed back to the previous version for the following reasons: * The identity function is in general not multiplicative. Only in the special case of ''M'' = positive integers could it be called a multiplicative function. But there are many other sets ''M'' out there. * We don't use colors in formulas * Blackboard bold is reserved for sets of numbers, like R or C. Letters that stand for functions, sets or variables are normally written in italic. user:AxelBoldt, Thursday, April 18, 2002
See other meanings of words starting from letter:
I
IA | IB | IC | ID | IE | IF | IG | IH | IJ | IK | IL | IM | IN | IO | IP | IR | IS | IT | IU | IW | IX | IY | IZ |Words begining with Identity_function:
Identity_function
Identity_function
These materials are based on Wikipedia and licensed under the GNU FDL
YouTube.com videos better site than Turbo Tax 2007
