{x, {y}}: {"x",{"y"}} |{{1,2}}|: 1 F!6: 8 {1,2,3} -> {6,7,8,9}: {1,2,3,6,7,8,9} F sub 3:5: {2,3,5} F sub 5:inf: {5,8,13,21,34,...} {x, {y}}: {"x",{"y"}} |{{1,2}}|: 1 F!6: 8 {1,2,3} -> {6,7,8,9}: {1,2,3,6,7,8,9} F sub 3:5: {2,3,5} F sub 5:inf: {5,8,13,21,34,...} {x, {y}}: {"x",{"y"}} |{{1,2}}|: 1 F!6: 8 {1,2,3} -> {6,7,8,9}: {1,2,3,6,7,8,9} F sub 3:5: {2,3,5} F sub 5:inf: {5,8,13,21,34,...} Fibonacci sequence: {1,1,2,3,5,8,13,21,34,55,...} closure of a,b,c: {"","a","b","c","aa","ab","ac","ba","bb","bc",...} [i]: {1,2,3,4,5,...} [i - 1]: {0,1,2,3,4,...} [i ^ 2]: {1,4,9,16,25,...} [i mod 3]: {1,2,0,1,2,...} [a to i]: {"a","aa","aaa","aaaa","aaaaa",...} [1]: {1,1,1,1,1,...} [aa]: {"aa","aa","aa","aa","aa",...} Fibonacci sequence: {1,1,2,3,5,8,13,21,34,55,...} closure of a,b,c: {"","a","b","c","aa","ab","ac","ba","bb","bc",...} [i]: {1,2,3,4,5,...} [i - 1]: {0,1,2,3,4,...} [i ^ 2]: {1,4,9,16,25,...} [i mod 3]: {1,2,0,1,2,...} [a to i]: {"a","aa","aaa","aaaa","aaaaa",...} [1]: {1,1,1,1,1,...} [aa]: {"aa","aa","aa","aa","aa",...} Fibonacci sequence: {1,1,2,3,5,8,13,21,34,55,...} closure of a,b,c: {"","a","b","c","aa","ab","ac","ba","bb","bc",...} [i]: {1,2,3,4,5,...} [i - 1]: {0,1,2,3,4,...} [i ^ 2]: {1,4,9,16,25,...} [i mod 3]: {1,2,0,1,2,...} [a to i]: {"a","aa","aaa","aaaa","aaaaa",...} [1]: {1,1,1,1,1,...} [aa]: {"aa","aa","aa","aa","aa",...} [Iplus:i]: {1,2,3,4,5,...} [Izero:i]: {0,1,2,3,4,...} [Fibseq:i]: {1,1,2,3,5,...} [[i ^ 2]:F]: {1,3,34,987,75025,...} [[i ** 2]:F]: {1,3,34,987} [{1,3,5}:Abc!i]: {"","b","aa"} Iplus \ 4: {1,2,3,4} [Iplus \ 4:Abc!i]: {"","a","b","c"} [Iplus:i]: {1,2,3,4,5,...} [Izero:i]: {0,1,2,3,4,...} [Fibseq:i]: {1,1,2,3,5,...} [[i ^ 2]:F]: {1,3,34,987,75025,...} [[i ** 2]:F]: {1,3,34,987} [{1,3,5}:Abc!i]: {"","b","aa"} Iplus \ 4: {1,2,3,4} [Iplus \ 4:Abc!i]: {"","a","b","c"} [Iplus:i]: {1,2,3,4,5,...} [Izero:i]: {0,1,2,3,4,...} [Fibseq:i]: {1,1,2,3,5,...} [[i ^ 2]:F]: {1,3,34,987,75025,...} [[i ** 2]:F]: {1,3,34,987} [{1,3,5}:Abc!i]: {"","b","aa"} Iplus \ 4: {1,2,3,4} [Iplus \ 4:Abc!i]: {"","a","b","c"} [lambda(j)k + j]: {101,102,103,104,105,...} [F:lambda(j)k + j]: {101,101,102,103,105,...} [Abc:lambda(s)s || s]: {"","aa","bb","cc","aaaa",...} [lambda(j)k + j]: {101,102,103,104,105,...} [F:lambda(j)k + j]: {101,101,102,103,105,...} [Abc:lambda(s)s || s]: {"","aa","bb","cc","aaaa",...} [lambda(j)k + j]: {101,102,103,104,105,...} [F:lambda(j)k + j]: {101,101,102,103,105,...} [Abc:lambda(s)s || s]: {"","aa","bb","cc","aaaa",...} [lambda(i)[lambda(j) U!i || L!j]: {"Aa","Ab","Ba","Bb","Ca",...} [lambda(i)[lambda(j) U!j || L!i]: {"Aa","Ba","Ca","Ab","Bb",...} [Izero:lambda(j)[(Iplus %% j) \ (j + 1):i]]: {2,3,3,4,5,...} [lambda(i)[lambda(j) U!i || L!j]: {"Aa","Ab","Ba","Bb","Ca",...} [lambda(i)[lambda(j) U!j || L!i]: {"Aa","Ba","Ca","Ab","Bb",...} [Izero:lambda(j)[(Iplus %% j) \ (j + 1):i]]: {2,3,3,4,5,...} [lambda(i)[lambda(j) U!i || L!j]: {"Aa","Ab","Ba","Bb","Ca",...} [lambda(i)[lambda(j) U!j || L!i]: {"Aa","Ba","Ca","Ab","Bb",...} [Izero:lambda(j)[(Iplus %% j) \ (j + 1):i]]: {2,3,3,4,5,...} I + J: {101,202,303,404,505,...} {a, ab, c} || {c, b, a}: {"ac","abb","ca"} Abc || Abc: {"","aa","bb","cc","aaaa",...} {1,2,3,4} + {1,4}: {2,6} {a, ab, c} || {x}: {"ax"} I + J: {101,202,303,404,505,...} {a, ab, c} || {c, b, a}: {"ac","abb","ca"} Abc || Abc: {"","aa","bb","cc","aaaa",...} {1,2,3,4} + {1,4}: {2,6} {a, ab, c} || {x}: {"ax"} I + J: {101,202,303,404,505,...} {a, ab, c} || {c, b, a}: {"ac","abb","ca"} Abc || Abc: {"","aa","bb","cc","aaaa",...} {1,2,3,4} + {1,4}: {2,6} {a, ab, c} || {x}: {"ax"} [if I!i = 0 then {0} else {1}]: {1,1,0,0,1,...} [if I!i = 0 then 0 else 1]: {1,1,0,0,1,...} [if I!i = 0 then {0} else {1}]: {1,1,0,0,1,...} [if I!i = 0 then 0 else 1]: {1,1,0,0,1,...} [if I!i = 0 then {0} else {1}]: {1,1,0,0,1,...} [if I!i = 0 then 0 else 1]: {1,1,0,0,1,...} Red(Iplus \ 5,+): {1,3,6,10,15} [Red(F \ i,+)]: {1,1,2,1,2,...} [Red(Abc \ (i + 1),||)]: {"","a","","a","ab",...} Red(Iplus \ 5,+): {1,3,6,10,15} [Red(F \ i,+)]: {1,1,2,1,2,...} [Red(Abc \ (i + 1),||)]: {"","a","","a","ab",...} Red(Iplus \ 5,+): {1,3,6,10,15} [Red(F \ i,+)]: {1,1,2,1,2,...} [Red(Abc \ (i + 1),||)]: {"","a","","a","ab",...} [if Iplus!i mod 2 = 0 then Iplus!i]: {2,4,6,8,10,...} [if |Abc!i| mod 2 = 0 then Abc!i]: {"","aa","ab","ac","ba",...} [if i mod 2 = 1 then F!(i + 1) else F!(i - 1)]: {1,1,3,2,8,5,21,13,55,34,...} [if i mod 2 = 1 then Iplus!i + Iplus!(i + 1)]: {3,7,11,15,19,...} [if I!i = 0 then i]: {1,5,7} [if Iplus!i mod 2 = 0 then Iplus!i]: {2,4,6,8,10,...} [if |Abc!i| mod 2 = 0 then Abc!i]: {"","aa","ab","ac","ba",...} [if i mod 2 = 1 then F!(i + 1) else F!(i - 1)]: {1,1,3,2,8,5,21,13,55,34,...} [if i mod 2 = 1 then Iplus!i + Iplus!(i + 1)]: {3,7,11,15,19,...} [if I!i = 0 then i]: {1,5,7} [if Iplus!i mod 2 = 0 then Iplus!i]: {2,4,6,8,10,...} [if |Abc!i| mod 2 = 0 then Abc!i]: {"","aa","ab","ac","ba",...} [if i mod 2 = 1 then F!(i + 1) else F!(i - 1)]: {1,1,3,2,8,5,21,13,55,34,...} [if i mod 2 = 1 then Iplus!i + Iplus!(i + 1)]: {3,7,11,15,19,...} [if I!i = 0 then i]: {1,5,7} [Fib(i)]: {1,1,2,3,5,...} [Fibs(i)]: {"a","b","ba","bab","babba",...} [G(i - 1)]: {0,1,1,2,3,...} [Izero:G(i)]: {0,1,1,2,3,...} [Izero:Gk(i,2)]: {1,2,2,2,3,...} [Fib(i)]: {1,1,2,3,5,...} [Fibs(i)]: {"a","b","ba","bab","babba",...} [G(i - 1)]: {0,1,1,2,3,...} [Izero:G(i)]: {0,1,1,2,3,...} [Izero:Gk(i,2)]: {1,2,2,2,3,...} [Fib(i)]: {1,1,2,3,5,...} [Fibs(i)]: {"a","b","ba","bab","babba",...} [G(i - 1)]: {0,1,1,2,3,...} [Izero:G(i)]: {0,1,1,2,3,...} [Izero:Gk(i,2)]: {1,2,2,2,3,...}