I have a book with denumerably many numbered pages; i.e, page 1, page 2, page 3, ... page n
On each page is written down a description of a set of positive integers
Describe a set of positive integers that cannot be described on any page of the book.
2006-06-18 18:25:10 · 3 answers · asked by Scott R 6 in Science & Mathematics ➔ Mathematics
ONCE YOU HAVE AN ANSWER.....!!!
Suppose your very description occurs on some page of the book-say page 10. Is 10 a member of that set or not? You will probably reach the absurdity that 10 is a member of the set only if 10 is not a member of the set. How can that be?
2006-06-18 18:39:08 · update #1
pages sequential for simplicity
2006-06-18 19:09:51 · update #2
nickipettis and Eulercrosser,
You are both correct.
Note that each can be refined to the set of all n such that n is not a member of the set on page n, not just all of them.
Using that however, can you resolve the corollary ?
2006-06-18 19:30:19 · update #3
i don't remember the notation, but it is
the set of Integers not found on pages p sub 1 through p sub n
2006-06-18 18:30:31 · answer #1 · answered by nickipettis 7 · 1⤊ 0⤋
All all the pages different? I was thinking of some sort of subset of sets thing, but since it has to be a set of integers, I think the best answer is the set of integers where the integer is not in the union of all the sets.
2006-06-19 02:08:43 · answer #2 · answered by Eulercrosser 4 · 0⤊ 0⤋
The set of all numbers that take up more characters then will fit on a single page
2006-06-19 01:29:08 · answer #3 · answered by pechorin1 3 · 0⤊ 0⤋