Recent content by MIB

I teach myself mathematics, but I want also to broaden my knowledge with some physics, which I think will enhance my intuition for different things in mathematics. The problem is that it seems I know nothing about physics. So I want you to recommend me which book(or books) must I read to develop...

Please , I want you to recommend me to a book on probability , I a have never read a probability book , or have a good background , I only Know what are probability measures , some theorems concerning it . I want a book that take me from the elementary probability , to advanced probability...

OK I restated it as following let f : (a,b) → ℝ be a differentiable function , suppose that f' is bounded , and that f has a root r in (a,b) . suppose that for x ≠ r , Jx denote the open interval between x and r , where if f(x) > 0 then f is convex on Jx , and if f(x) < 0 then f is concave on...

I know it can be very hard to think an example where the derivative vanishes at a point which is not a root , and I think it is impossible the problem is that it says " for any x0 in (a,b) the Newton sequence converges to a root where x0 is it initial point " , and then this wrong ,because the...

I think we must replace "f' is bounded on (a,b)" by "f' is non-zero throughout (a,b)"

I think there is some thing wrong in this exercise which I met by chance in a book of Calculus and analysis while looking for rigorous definition for angle , it says let f : (a,b) → ℝ be a differentiable function , suppose that f' is bounded , and that f has a root r in (a,b) . suppose...

to our intuition we see that there is no number that if we multiplied by itself will be negative , since if it is negative then squaring it will result in a positive number , and the same for positive numbers , precisely we see that from the properties of the order field of real numbers that if...

ok must I begin know to prove the generalized theorem with this background in Mathematics ?

no , I don't know it , but if I knew , I would put X as the set of 1/Q , where Q is a natural number and the number 0 , and the accumulation point is 0

yes , In fact I am using this to prove the uniqueness of the representations of functions as a power series , I yes I know about power series and series of functions and sequences of functions ... etc

Is that true ? Let be \Sigma_{n=1}^{\infty} a_n a series in ℝ .Suppose that \Sigma_{n=1}^{\infty} a_n is absolutely convergent . Suppose that for each Q \in N , \Sigma_{n=1}^{\infty} \frac{a_n}{Q^n} is convergent and \Sigma_{n=1}^{\infty} \frac{a_n}{Q^n} = 0.Then a_n = 0 for all n \in N...

why substitution method for integration always work ? Why can we completely treat dx and du known in substitution method completely like differentials even if we don't have ∫f(g(x))g'(x) dx , i.e : why we can substitute x in terms of u and dx in terms of du . thanks

another question please , when I want to prove statements like that \lim_{x \to a} f(x) = \lim_{h \to 0} f(a+h) MUST I prove the two following statements or one of them is enough 1 - Assume that \lim_{x \to a} f(x) = L , and peove that given ε > 0 , there exists δ > 0 such that ...

IS This argument is right

Now I think that all what I say in the end was useless but I am not sure , the definition says that if a function f is defined on some open containing a except possibly at a , then we write \lim_{x \to a} f(x) = L if for every ε > 0 , there exists positive number δ such that if...