Mathematics Homework Solutions

Real analysis

Prove that if a is an upper bound for A and if a is also an element of A, then it must be that a=sup A

Posting ID: 25325

square root theory proof

Pove that : 1)A real number y <0 has no square root. 2)he number y= 0 has exactly one square root , namely 0. 3)A real number y>0 has exactly two square roots, one positive and one negative. Proof: 1) Proof by contradiction when y<0 , assume that y has a square root . Then number x is called square root of y if x^2 ...continues

Posting ID: 25331

Real Analysis

Proof: Given any two real numbers a

Posting ID: 25355

Real Analysis

proof: if A subset or equal of B and B is countable, then A is either countable, finite or empty.

Posting ID: 25356

Real Analysis

verify the triangle inequality in the special cases where: 1-a and b have the same sign 2-a>=0, b<0, and a+b>=0

Posting ID: 25357

Bernoulli's inequality

Suppose that -1 < r < 1. Prove that r^m -> 0 as m -> infinity. (I think you can write 1/r in the form 1+y, where y>0. Also I believe you can use the Bernoulli's inequality (1+y)^m >= 1+my for all m belonging to N(natural numbers))

Posting ID: 25385

Real Analysis

1- if A1,A2,A3,...,Am are each countable sets, then the union A1 U A2 U A3...U Am is countable 2- if An is a countable set for each n belong to N,then Un=1(to infinity) An is countable

Posting ID: 25452

Real Analysis

Show that the set of all finite subsets of N is a countable set

Posting ID: 25453

Real Analysis

using the definition of convergence of a sequence show thatthe following sequence converge to the proposed limit: 1-lim 1/(6n^2+1)=0 2-lim 2/sqrt[n+3]=0 3-lim (3n+1)/(2n+5)=3/2

Posting ID: 25454

Real Analysis

let[[x]] be the greatest integer less than or equal to x. for example [[Pi]]=3 and [[3]]=3. Find lim an(small n) and supply proofs for each conclusion if a) an=[[1/n]] b) an=[[(10+n)/2n]]

Posting ID: 25455
Browse