Prove that positive real numbers correspond bijectively

Here is the problem: Prove that positive real numbers correspond bijectively to decimal expansions not terminating in an infinite string of 9's as follows. The decimal expansion of is where N is the largest integer smaller than is the largest integer is the largest integer and so on. (a) Show that each is a digit b ...continues

Prove same cardinality

Prove that Rsquared has the same cardinality of R (hint: think of shuffling two string of digits) See attachment for full question

Define injections f

Define injections f:... (see attachment)

Real Analysis.2.1

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USE INDUCTION; analysis

What is the graphical relationship between z and -iz?

matlab

I have version 4 of matlab and I have been doing research using excel. I have all the point and now I would like to use matlab to make a graph of the topography of the tank. I would like some one to show me how to do it because I don't understand how to plot all the points. Can some one give me a 3D graph of the topography? wi ...continues

Real analysis (measurable functions)

Q1. If 0<=a_1<=a_2<=a_3<=....,( 1,2,3 are the subscripts of a) 0<=b_1<=b_2<=b_3<=......(1,2,3 are the subscripts of b) and a_n --> a and b_n -->b Then prove that a_n*b_n -->a*b Q2.Let f: R --> R be monotonically increasing, i.e. f(x_1)<= f(x_2) for x_1< = x_2. Show that f is measurable. Hint: You may extend f to f':[-in ...continues

Discrete Math - Probability (Void)

In the game of bridge, a player is dealt a hand of 13 playing cards from a standard 52 card deck. A hand is said to have a void in a suit if it contains no cards in that suit. Determine the number of distinct hands containing at least one void. What is the probability of being dealt a hand with at least one void? Your answer sho ...continues

Laplace Transform - Show that the Laplace transform......

Let f be a piecewise continuous function on [0,T]. Define f on the whole of [0,inf) by f(t+nT) for all t and all integer n. Show that the Laplace transform if f is given by L[f(t)] = 1/[1-exp(-sT)]*int(exp(-st)*f(t)dt,t=0..T) By taking the Laplace transform and using the convolution theorem, obtain the solution of ...continues

Real Analysis

given a function f and a subset A of its domain, let f(A) represent the range of f over the set A; f(A)={f(x) : x belong to A}. a-Let f(x)=x^2. If A=[0,2](the closed interval{x belong to R : 0<=x<=2}) and B=[1,4],find f(A) and f(B).Does f(A intersection B)=f(A) intersection f(B) in this case?.Does f(A U B)=f(A) U f(B)?. b-Fi ...continues