Computable real function

In mathematical logic, specifically computability theory, a function f : R → R {displaystyle fcolon mathbb {R} o mathbb {R} } is sequentially computable if, for every computable sequence { x i } i = 1 ∞ {displaystyle {x_{i}}_{i=1}^{infty }} of real numbers, the sequence { f ( x i ) } i = 1 ∞ {displaystyle {f(x_{i})}_{i=1}^{infty }} is also computable. In mathematical logic, specifically computability theory, a function f : R → R {displaystyle fcolon mathbb {R} o mathbb {R} } is sequentially computable if, for every computable sequence { x i } i = 1 ∞ {displaystyle {x_{i}}_{i=1}^{infty }} of real numbers, the sequence { f ( x i ) } i = 1 ∞ {displaystyle {f(x_{i})}_{i=1}^{infty }} is also computable. A function f : R → R {displaystyle fcolon mathbb {R} o mathbb {R} } is effectively uniformly continuous if there exists a recursive function d : N → N {displaystyle dcolon mathbb {N} o mathbb {N} } such that, if | x − y | < 1 d ( n ) {displaystyle |x-y|<{1 over d(n)}}