Hello everyone.
I am trying to prove that the in a planar domain U \subseteq C equipped with a metric \rho, the definition of the distance between P and Q, both lying in U is given by
\\ \\ d_{\rho}(P,Q)=inf \left\{ L_{\rho}(\gamma): \gamma \in C_{U}(P,Q)\right\},
where C_{U}(P,Q) denotes all...
Hi all.
The problem is "Prove that a function which is analytic in the whole plane and satisfies an inequality |f(z)| < |z|^n for some n and sufficiently large |z| reduces to a polynomial." I do not understand what I need to show that the function reduces to a polynomial.
Any help will be...
Earlier when calculus was invented by newton and leibniz, then such questions of rigor was absent, or they did not have the right tools for the precise definitions of continuity, until weierstrass. But then as mathematicians looked carefully at these concepts, they were not satisfied with just...
So the proof involves bisection of the intervals. We start with interval [a,b], where f(a)>0 and f(b)<0. Now we bisect the inteval and consider f((a+b)/2). If the function value at the midpoint is +ve then we select the interval [(a+b/2),b], else the interval [a,(a+b)/2]. So in this way we get a...
The Bolzano theorem, which is a special case of intermediate value theorem, states that if you have a continuous function on an interval [a,b], such that f(a) is positive and f(b) is negative, then there must exist a point "c" belonging to the interval (a,b) where f(c)=0.
Continuity is...
Hi all,
How do I prove that the set of all Mobius Maps form a simple group, that is they have no non-trivial subgroup? How can I characterize a non-trivial subgroup? Hints will be welcome.
Thanks
Hi all,
If I have to prove that the graph G and its complement G' are isomorphic, then is it enough to prove that both G and G' will have the same number of edges. Intuitively its clear to me, but how do I prove this. If there's a counterexample, please post.
Thanks in advance.
(Well I don't know if this post should be here or not. If not please move it to the appropriate place.)
Hi Everyone.
Next year International Congress of Mathematicians will be held in Hyderabad, India. And I am 2nd Yr undergraduate student in mathematics, and I wish to attend it. The thing I...
And also because that we wish that square-root should be a "function", and for being a function it has to be defined like that only. By definition, a function takes a value from a set A and maps it into B, and no two numbers in A can map to the same number in B.
thanks buddies..I will surely try to get my hands on the book..
by the way, why was the last post deleted that gave a proof to my question?? Was that proof okay?
Well, I have just passed my high school and will be going in undergraduate course this year. therefore i don't know Peano axiom in detail. I think i have to study abstract algebra.Will that help me? Also, can i have a suggestion of a good introductory book treating the subject in detail as well...