Recent content by trash

Homework Statement Consider the differential equation y'=x-y^2. Find maxima, minima and critical points; show that for every solution f=f(t) exists T\geq 0 such that f(t)< \sqrt{T}\;\forall t > T Homework Equations The Riccati equation: y'=a(x)y^2+b(x)y+c(x) The Bernoulli equation...

Thanks a lot. Just for clarification, my worry comes mainly because of the product. I'm trying to deal with an intuitive way to think about the infinity in this case, I thought the problem was how I defined the function g_k, because I defined an injection to the set of...

Homework Statement Let A=\{f:\mathbb{Z}\to\mathbb{Z}: f(n)\neq 0 \text{for a finite number of n}\}, prove that A is countable. Homework Equations I'm considering using that it would be equivalent to prove that the set A'=\{f:\mathbb{N}\to\mathbb{N}: f(n)\neq 0 \text{for a finite number...

I'd like to know if it is possible to define a bijection between the sets [0,1]^{\mathbb{Z}} and [0,1]^{\mathbb{N}}; \mathbb{N}^{\mathbb{N}} and \mathbb{Z}^{\mathbb{Z}}. I tried to define a bijection between [0,1]^\mathbb{N} and [0,1]^\mathbb{Z} as follows: Take the bijection...

Yes, you're right. I'm sorry, I read it too fast and didn't think it through :frown:

Thanks a lot, now that makes sense. Still, for the last example if f_1(1)=1 wouldn't be f(1)=2 which exceeds the domain?, maybe something like f(x)=[f_n(1/n)]/2 would work better?.

Thanks a lot. But that was my mistake. The proposition is about the set of functions from [0,1] to \mathbb{Z}

I'm reading about countable and uncountable sets, I found the following statement: "The set of the functions from \mathbb{Z} to [0,1] is uncountable" with the following proof: "To see that, suppose the set countable having the list \{f_1,f_2,\dots\} and define f(x) = f_n(1/n) if x=1/n and f(x)=0...

Thanks for answring AlephZero. I have to enter the whole thing before i get the answer, that's what the exercise ask for. If i don't process the whole thing wouldn't it go like this? [Enter a] Nothing happens [Enter a] Nothing happens [Enter a] Nothing happens [Enter f] prints a=3...

I'm working with this exercise: make a program that gives the number of consecutive letters of a word and the most repeated letter in a row -example: if i enter aaafdseergftth and i press return the program should return a = 3, e=2, t=2 and a=3-. I've come up with a couple of "solutions"...

Homework Statement Given a sequence of independent random variables {X_n}, each one with distribution Exp(1). Show that Y_n = \displaystyle\frac{X_n}{\log(n)} with n \geq 2 converges to 0 in probability but it doesn't coverges almost surely to 0. Homework Equations Density for each X_n...

Thanks, both of you. Let me give it a try: >What is the probability that the man visited just 2 cities after n visits? He's in a random city and travel to another random city, then if he chooses always the city he already visited from a total of three, then P{"the man visited just 2...

Homework Statement A man wants to travel to four cities (A,B,C,D) but he has such a bad memory that he can't remember the cities that visited, therefore, if he travel to city A he can choose between (B,C,D) and if he then travel to B he can choose between (A,C,D). Find v, If v it's the...