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It,,is,,concerned,,with,,the,,parts,,of,,real,,analysis,,and,,functional,,analysis,,that,,can,,be,,carried,,out,,in,,a,,computable,,manner.,,27,2.3,Standard,Representations,of,Sets,of,Continuous,String,Functions,.,The,,,equality,,,relation,,,on,,,computable,,,real,,,numbers,,,is,,,not,,,computable,,,,but,,,for,,,unequal,,,computable,,,real,,,numbers,,,the,,,order,,,relation,,,is,,,computable.,,,Computability,on,Closed,,Open,and,Compact,Sets,5.1,Closed,Sets,and,Open,Sets,.,A,function,f,:,R,→,R,{displaystyle,fcolon,mathbb,{R},to,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.,

Spaces,of,Continuous,Functions,6.1,Various,representations,.,Main,article:,Computable,real,function.,143,,,.,,,Computable,,numbers,,are,,the,,real,,numbers,,that,,can,,be,,computed,,to,,within,,any,,desired,,precision,,by,,a,,finite,,,terminating,,algorithm.,,2,,1.3,,A,,Sketch,,of,,TTE,,.,,The,field,is,closely,related,to,constructive,analysis,and,numerical,analysis.,

190,,.,,195,,7.2,,Complexity,,Induced,,by,,the,,Signed,,Digit,,Representation,,.,,In,mathematics,and,computer,science,,computable,analysis,is,the,study,of,mathematical,analysis,from,the,perspective,of,computability,theory.,4,1.3.3,Computable,Real,Numbers,and,Functions,.,Computability,on,the,Real,Numbers,4.1,Various,Representations,of,the,Real,Numbers,.,Basic,,,results.,,,Naming,,,Systems,,,3.1,,,Continuity,,,and,,,Computability,,,Induced,,,by,,,Naming,,,Systems,,,.,,,33,,,2.4,,,Effective,,,Subsets,,,.,,,43,.,