There are examples of real valued functions which are continuous at irrationals and discontinuous at rationals. But i am trying to find such a monotone function. I don't know how to think this types of examples. I wants such types of simple examples not too much complicated so that each and everyone can easily digest it. I tried many simple examples but did't got. In the book Counterexamples in Analysis by Bernard R. Gelbaum and John Meigs Hubbell Olmsted there is given a way to construct such types to examples, but i like simplest such types of example. Please try to give such type of example. Thanks in advance.
Subscribe to:
Post Comments (Atom)
analysis - Injection, making bijection
I have injection $f \colon A \rightarrow B$ and I want to get bijection. Can I just resting codomain to $f(A)$? I know that every function i...
-
Find all integer solutions of $2n \equiv 12 \bmod 19$ So I have re-arranged to: $2x-19y=12$ and by the extended Euclidean Algorithm, I get $...
-
Find the limit of the following-$$\lim\limits_{n \to \infty}\frac{2^{-n^2}}{\sum\limits_{k=n+1}^{\infty} 2^{-k^2}}$$ My work: We can see t...
-
I understand that a continued fraction of the form: $g(n_1,n_2,n_3,n_4,n_5,\ldots)= n_1 + \cfrac{1}{n_2 + \cfrac{1}{n_3 + \cfrac{1}{n_4 + \c...
No comments:
Post a Comment