# Set Theory, Logic, Probability, Statistics

- Fundamentals: Set theory, logic and proofs. Probability and statistics
 Meta Thread / Thread Starter Last Post Replies Views Views: 654 Announcement: Follow us on social media and spread the word about PF! Jan16-12 Please post any and all homework or other textbook-style problems in one of the Homework & Coursework Questions... Feb23-13 09:25 AM micromass 1 32,454 mathworld defines the paradox like this:"Even though real arithmetic is uncountable, it possesses a countable... Oct17-03 05:54 PM Hurkyl 1 2,372 i found in this paper the term in the title: http://arxiv.org/abs/math.GR/9305201 what can you tell me about them?... Apr12-04 02:19 PM matt grime 1 2,584 in this page ive encountered this topic (it's a topic from combinatorics, so it's relevant to discrete maths with sets... Jul2-05 03:23 AM MathematicalPhysicist 3 1,648 prove that \epsilon_0 is an \epsilon number and that it's the smallest number. \epsilon_0=\lim_{n<\omega}\phi(n)... Aug30-06 03:18 AM matt grime 1 1,540 i searched at amazon for books, and find some books about this topic, and i wonder what does this topic cover? in one... Apr19-06 03:11 PM Hurkyl 3 1,874 1)let P={p1,p2....} be the set of all prime numbers for every n natural, present n as a representation of its prime... Apr27-06 02:20 PM HallsofIvy 33 2,698 i have a few question, that i hope they will answered. 1) let w={0,1...,n,..}={0}UN, and let f:wxw->w such that the... Jun15-06 02:21 PM CrankFan 18 1,645 i need to prove that if x is the first of sub(\phi;a,\psi) then there exists 1<=i<=n and there exist firsts \phi' of... Jul23-06 08:55 AM MathematicalPhysicist 1 1,989 i read that there are some logicians who do not use the axiom of choice in their axioms systems. i wonder what is the... Aug31-06 02:16 AM MathematicalPhysicist 2 1,382 what are the current open problems in logic? in model theory, proof theory and philosophical logic? and what are the... Oct9-06 03:14 AM matt grime 4 2,074 i think that i read that the compactness theorem in logic has a similar theorem in topology. i wanted to inquire, are... Nov10-06 07:24 AM HallsofIvy 3 2,142 how do i show that Y^(XU{x})=(Y^X)x(Y^{x}) where X and Y are finite sets, and {x} is a singleton. obvisouly i need to... Nov18-06 06:43 AM matt grime 4 1,092 i have a function f:R->R where f is monotone increasing, i need to show that the set of discontinuous points of f is... Dec7-06 12:42 PM HallsofIvy 5 4,604 i have a function f:A->B, im also given that |B|<=null aleph, and for every b in B, |f^-1({b})|<=null aleph, i need to... Dec11-06 12:33 PM MathematicalPhysicist 2 1,650 1. i need to show that the set A={x in Q|0<=x<=1} Q is the rationals set. can be covered by open intervals I_k (k is... Dec28-06 11:59 AM EnumaElish 34 3,983 i need to find the cardinality of the set of all concave polygons. i know that each n-polygon is characterized by... Dec30-06 08:01 AM MathematicalPhysicist 12 2,188 i need to find the cardinality of set of continuous functions f:R->R. well i know that this cardinality is samaller... Jan1-07 03:34 AM AKG 14 6,799 i need to prove that there are c sqequences of rational numbers. basically, i need to show that |Q^N|=c. here, are a... Jan4-07 07:13 AM HallsofIvy 3 1,382 i need to show that there exists a class of sets A which is a subset of P(Q) such that it satisfies: 1) |A|=c (c is... Jan8-07 11:47 AM MathematicalPhysicist 14 2,562 i need to prove that X is an infinite set iff for every function f:X->X there exists a proper nonempty subset A of X... Feb15-07 04:25 PM AKG 6 1,847 i need to prove the next statement: let D be infinite class of infinite subsets of natural numbers that satisfies the... Feb13-07 07:19 AM ecurbian 5 1,478 1)axiom of choice: prove that for every set X and for every f:X->X there exists g:X->X such that fogof=f. 2)zorn's... Feb13-07 08:52 AM MathematicalPhysicist 0 1,066 let R be a reflexive and symmetric relation on a set X. let's define a relation S on X. by (x,y) in S iff there exists... Feb14-07 10:07 AM MathematicalPhysicist 0 1,931 suppose our language contains one unary syombol function. we are given the next 5 models: A= B=... Mar31-07 09:24 AM MathematicalPhysicist 2 1,412 let r>1 which term in (x1+...+xk)^rk has the greatest coefficient? well i have this equation: ... Apr9-07 05:29 AM MathematicalPhysicist 1 3,287 let a\in R and Q>=3 where Q\in Z, i need to prove that in the set {a,2a,...,(Q-1)a} there exists a number which its... Apr30-07 02:01 PM AKG 9 2,149 my question is as follows: how many words with n letters, you can construct with A,T,G,C such that ACT and TTT will... Jun15-07 04:45 AM MathematicalPhysicist 0 1,257 question in model theory. let L={P_n|n \in N} every P_n is an unary predicate. let's define a theory that says... Jun17-07 10:50 AM MathematicalPhysicist 0 1,129 I need to find: 1. let n be a natural number compute the number of permutations s:{1,...,3n}->{1,...,3n} on 3n terms... Jul2-07 02:05 AM MathematicalPhysicist 8 1,391 how many words of length k can you create from {1,...,k} such that 1 appears even number of times? well, for k=0 we... Jul2-07 06:05 AM MathematicalPhysicist 5 1,992 My problem is as follows: Prove that the set of Godel numbers of provable formulas (P_f) is recursive iff the set of... Dec18-07 12:03 PM MathematicalPhysicist 0 1,985 I'm not sure I understnad what is a marginal distribution, but i need to show that if F1,F2 are one dimensional... Feb9-08 03:41 PM EnumaElish 1 2,413 Let X,Y~U(0,1) independent (which means that they are distributed uniformly on ). find the distribution of U=X-Y.... Feb29-08 08:03 PM quadraphonics 2 4,959 I have a graph G with n vertices, with connectivity \kappa(G)=k i.e its k- connected, I need to show that ... Dec1-10 07:08 PM ych22 4 1,304 I need help with question number 8, I thought I had it right the proof of the lower bound, but now I see my solution... Dec8-10 02:01 AM MathematicalPhysicist 0 754 I am given a graph G with 1000 vertices and 250,001 edges and I need to show there are two triangles in it with common... Jan16-11 03:20 PM MathematicalPhysicist 1 806 I have the next two signals: X(t) and G(t) and a random process Y(t)=G(t)X(t) where X(t) and G(t) are wide sense... Apr5-13 11:12 PM MathematicalPhysicist 3 529 Hi, I have the next RV: $$\underline{W}=\frac{\underline{X}}{\frac{||\underline{X}||}{\sqrt{n}}}$$ where X_i... May20-13 03:01 PM mathman 1 516 Hey everyone, I have a question regarding combinations and poker! Could someone explain to me why the number of... Apr21-12 09:57 AM Stephen Tashi 3 1,436 What are the current capabilities of modern Theorem Provers? I know about logic/undecidability/complexity theory so go... Feb5-14 11:39 AM Hornbein 4 401