Following is a list of some decimal numbers set up in a correspondence with the
ID: 3120755 • Letter: F
Question
Following is a list of some decimal numbers set up in a correspondence with the first few natural numbers. Describe Cantors diagonalization method argument, and write down the first five digits of a number that Cantors argument produces1 - 0.436827384... 2 - 0.728458988... 3 - 0.433378349... 4 - 0.444444444... 5 - 0.222222222... Following is a list of some decimal numbers set up in a correspondence with the first few natural numbers. Describe Cantors diagonalization method argument, and write down the first five digits of a number that Cantors argument produces
1 - 0.436827384... 2 - 0.728458988... 3 - 0.433378349... 4 - 0.444444444... 5 - 0.222222222... Following is a list of some decimal numbers set up in a correspondence with the first few natural numbers. Describe Cantors diagonalization method argument, and write down the first five digits of a number that Cantors argument produces
1 - 0.436827384... 2 - 0.728458988... 3 - 0.433378349... 4 - 0.444444444... 5 - 0.222222222... 1 - 0.436827384... 2 - 0.728458988... 3 - 0.433378349... 4 - 0.444444444... 5 - 0.222222222...
Explanation / Answer
Cantors diagonalization method argument: There are infinite sets which cannot be put into one-to-one correspondence with infinite sets of natural numbers;
Suppose we take the first digit from first sequence;
second from second
third from third and take complementary digit (any digit which is not equal to given digit)
the sequence will not match any given sequence;
as digits in diagonal are {4,2,3,4,2}
the sequence 0.84196 does not corresponds to any given sequence;