1. A

    Club Sets and Fodor's Lemma

    I'm trying to obtain a better understanding of what a club set is to get started. I understand what it means for a set to be unbounded with respect to a limit ordinal $\kappa$, but I'm having trouble grasping what it means for a set to be closed in $\kappa$...
  2. S

    Pumping Lemma question

    Help Can someone advice best way to answer this question with the help slides
  3. P

    Academic Guidance A lemma which is a special case of a theorem

    It is often the case that a theorem is called using a lemma which in turn is an easy consequence of the theorem (in other words, is a special case of the theorem). Which term could you suggest specifically for such a lemma? I think about using my own coined word (like "specialia") to...
  4. E

    Refinement of Schwartz's Lemma

    Looking for how to prove the refinement of Schwartz's Lemma. in number 3.
  5. P

    Zorn lemma

    What the differences between the Zoran lemma and Axiom of Choice?
  6. N

    ito lemma

    Assuming a stock with alpha 0.14, delta 0.01 and volatility of 0.48, how do I derive the price process of a derivative with value V = S^(1/1)e^(0.4)*(1-t) [Equation 1], by using Ito lemma (equation 2)? Ito lemma (equation 2): Where Vs = first derivative of [equation 1] Vt is the first...
  7. G

    Urysohn's Lemma

    Hello. This did not come from a topology book, but we were asked to prove Urysohn's Lemma. We are familiar with standard proofs for this, which are all likely simpler to exhibit than our attempt here, but we were just curious about where our method here went wrong. At a glance, the lemma...
  8. B

    L = { $a^nb^mc^n | m \ge n$ } is not context free. With Pumping Lemma through 6 cases

    This is the Pumping Lemma for Context Free Languages I refer: And this is the exercise I encounter some problems: $L = \left \{ a^nb^mc^n \mid m \ge n \right \}$ is not context free. Proof- by contradiction using the pumping lemma for context-free languages. Assume that $L$ is...
  9. S

    question about probabilistic methods and isolation lemma.

    Given the set $\mathcal{F}\in\mathcal{P}(\{1,...,m\})$, I need to provide it with probability $\frac{1}{2}$ a weight function $w:\{1,...,m\}\rightarrow\{1,...,n\}$ such that there will be a single minimal $F\in\mathcal{F}$. The problem is that we are not given what $\mathcal{F}$ and $m$ are...
  10. B

    proving a lemma

    Need to proof it: Assume s ∈ R is an upper bound for a set A ⊆ R. Then, s = sup A if and only if, for every choice of ε > 0, there exists an element a ∈ A satisfying s − ε<a. Can "a" depend on s ? for example, a = s- ε/2
  11. J

    Frege's 0 Lemma is not a definition of zero

    Gottlob Frege's definition of 0 in In λ-notation is 0 = #[λx x≠x]. In words it means 0 is the number of the property of x such that x is not self identical (# signifies 'number', [] 'property', λx 'x such that', and x≠x is the condition). Please see Proof of Lemma Concerning Zero...
  12. B

    Reverse Fatou Lemma

    Let $(\Omega, \mathcal{F}, \mathbb{P})$ be probability space and ${E}_{n} \in \mathbb{N}$ be $\mathcal{F}$-measurable sets. Show example that reverse Fatou's Lemma, $\mathbb{P}(\limsup_n E_n)\geq \limsup_n \mathbb{P}(E_n)$, meets inequality strictly. I understand this inequality of inf...
  13. C

    Weierstrass' 7th Lemma

    I have a question regarding a property of a cubic function's graph. Suppose that the function f(x) has two stationary points, x1 and x2 = x1 + 2a, i.e. the distance between them is 2a. Then f(x1 - a) = f(x2) and f(x2 + a) = f(x1). This is handy when sketching the graph of a cubic...
  14. S

    Farkas Lemma

    Hi, I have following problem: I have a Polyhedra P:\{x:2x_1+3x_2\le 27 , 2x_1-2x_2\le 7, -6x_1-2x_2\le-9, -2x_1-6x_2\le -11, -6x_1+8x_2\le 21\} I have to show with the Farkas Lemma that the inequality x_2\le 6 holds for every x in P.... i have plotted P and can show grafically that...
  15. T

    Proving a lemma about Binomial distributions

    Hello to all. I'm trying to prove some lemma about Binomial distributions, as a part of a larger prove, but I just can't succeed in proving it, although it seems obvious to me. The lemma is: There are given two Binomial distributions A', B' which share the same number of repititions, say t(n)...
  16. A

    Explanation of the proof of a lemma of Asymptotic analysis

    Hi I've read this lemma in my book: Can anyone explain me the part p(n)??(n^k) of the proof? Why should we divide a_k*n^k by 2? Why can't we take a_k*n^k as coefficient of n^k? And how do we obtain that n>2A/a_k? Please help! Thanks! :D
  17. J

    Little LCM lemma for the first n pronics

    Pronics are of course numbers of the form (x)(x+1). The first pronic can for different purposes be considered 0*1 or 1*2. In this case, I am going with 1*2 as the first pronic. First n pronics will therefore be 1*2, 2*3, ..., n(n+1) ALL pronics are even, as one of n and n+1 is always even. But...
  18. T

    Pumping Lemma for palindromes

    Hi, I'm having some difficulties proving pumping lemma problems. Even when I have an idea about how the problem can be solved, I can't seem to use the correct notation to express the solution. Prove \{ww | w \in \{0,1\}*\} is not regular. Let L = \{ww | w \in \{0,1\}*\}. Assume that L is a...
  19. X

    Problem about the proof of Riemman-Lebesgue Lemma

    I do not understand the particular part of the proof of Riemann-Lebesgue lemma. (red-underlined in the attachment image) [attachment=0:2c11342v]kurser.math.su.se-file.php-628-Riemann-Lebesgue-Vretblad.pdf.png[/attachment:2c11342v] If I is not compact, f is absolutely integrable, e>0 be...
  20. D

    How can I illustrate this lemma correctly?

    Hi all, I can calculate diophantic equations and solve them pretty well generally but when it comes to illustrating proofs and lemmas I really get stuck. The lemma is : Let a,b be elements of Z. If d|a and d|b and k,l are also elements of Z then d|(ka + lb). What does all the letters above...