Perfect set is that all it's limits are obtained in itself, it doesn't need any other real number that doesn't belong to it. Doesn't depend on its exterior. human beings depend on others , that is why people say it is perfect 😀
Sir, if x belongs to C it belongs to each C_n, according to the definition of cantor set, Sir if n---> infinity, then C is going to contain only the end points of all the intervals in each C_n, all are rational numbers. C = { 0,....1/9,1/3,........2/3, 1} it is a subset of rational numbers it has to be countable, difference of rational numbers is always rational, as C is perfect it can't have an irrational limit point. C is not going to contain irrational numbers, if we take n finite only then Cantor's set would be perfect and uncountable
Excelente explicacion mi querido profesor, recomiendem un libro por favor, estoy interesado en solo el conjunto de Cantor, saludos desde Venezuela
Perfect set is that all it's limits are obtained in itself, it doesn't need any other real number that doesn't belong to it. Doesn't depend on its exterior. human beings depend on others , that is why people say it is perfect 😀
Thanks sir.. Your videos are awesome..
There is one closed interval that is not perfect. It’s the closed interval containing just one point which makes it finite of course.
thx man, saved me
Sir, if x belongs to C it belongs to each C_n, according to the definition of cantor set,
Sir if n---> infinity, then C is going to contain only the end points of all the intervals in each C_n, all are rational numbers.
C = { 0,....1/9,1/3,........2/3, 1} it is a subset of rational numbers it has to be countable, difference of rational numbers is always rational, as C is perfect it can't have an irrational limit point. C is not going to contain irrational numbers, if we take n finite only then Cantor's set would be perfect and
uncountable