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In [[mathematics]], a '''finitary boolean function''' is a [[function (mathematics)|function]] of the form ''f'' : '''B'''^''k'' → '''B''', where '''B''' = {0, 1} is a ''[[boolean domain]]'' and where ''k'' is a nonnegative integer.  In the case where ''k'' = 0, the "function" is simply a constant element of '''B'''.

In [[mathematics]], a '''finitary boolean function''' is a [[function (mathematics)|function]] of the form <math>f : \mathbb{B}^k \to \mathbb{B},</math> where <math>\mathbb{B} = \{ 0, 1 \}</math> is a [[boolean domain]] and where <math>k\!</math> is a nonnegative integer.  In the case where <math>k = 0,\!</math> the function is simply a constant element of <math>\mathbb{B}.</math>

More generally, a function of the form ''f''&nbsp;:&nbsp;''X''&nbsp;&rarr;&nbsp;'''B''', where ''X'' is an arbitrary set, is a ''[[boolean-valued function]]''.  If ''X'' = '''M''' = {1,&nbsp;2,&nbsp;3,&nbsp;&hellip;}, then ''f'' is a ''binary sequence'', that is, an infinite [[sequence]] of 0's and 1's.  If ''X'' = [''k''] = {1,&nbsp;2,&nbsp;3,&nbsp;&hellip;,&nbsp;''k''}, then ''f'' is ''binary sequence'' of length ''k''.

More generally, a function of the form ''f''&nbsp;:&nbsp;''X''&nbsp;&rarr;&nbsp;'''B''', where ''X'' is an arbitrary set, is a ''[[boolean-valued function]]''.  If ''X'' = '''M''' = {1,&nbsp;2,&nbsp;3,&nbsp;&hellip;}, then ''f'' is a ''binary sequence'', that is, an infinite [[sequence]] of 0's and 1's.  If ''X'' = [''k''] = {1,&nbsp;2,&nbsp;3,&nbsp;&hellip;,&nbsp;''k''}, then ''f'' is ''binary sequence'' of length ''k''.