Pat Says

Ok, so we are given that {an} is the sequence 1/2, 1/3, 2/3, 1/4, 2/4, 3/4, 1/5, 2/5, 3/5, 4/5, 1/6, 2/6, .... Now, the problem says suppose that 0< a < b <1. Let N(n; a,b) be the number of integers j<n such that aj is in [a,b]. I can't figure out exactly what this means ( i.e. given any n, a, b what does it equal?) It does say that "Thus N(2; 1/3, 2/3) = 2, and N(4; 1/3, 2/3) = 3." Our actual job is to prove that lim n->infinity of [N(n; a,b)]/[n] = b-a. So, I can't begin to start the problem until I figure out what the question even means! Also, if the value is supposed to be an integer then how can the limit be b-a (a non integer.. for the most part)? By the way, I am assuming that n is supposed to be a natural number as it usually is in this book and seems to also be so in this context. If someone could just help explain how to figure out the value of any given a,b,n it would be greatly appreciated and at least give me something to work with. Thank you to everyone in advance. Note (in case it helps): On part b of the question it says that a sequence {an} of numbers in [0,1] is called uniformly distributed in [0,1], if the limit above holds.

Not according to religious beliefs. The statement that we are playing God by creating life from scratch is misleading. We would in fact not be creating life from scratch. This is because God is said to have created life from nothing. Technically we would be using God's creation to create life--not our own.

Lol, I think you should try reading the article... or at least the title of the article. Thanks for the link though. SkepticLance: Even when going to Mars you need to bring starter materials. On Venus you could use inflatable habitats and of course bring the necessary amount of food, water, etc. to start with. After that though, you can get all the major organic materials from the atmosphere. There is a lot of sulfuric acid and carbon dioxide in the atmosphere. Using the solar energy from the sun and also from the reflected light off the clouds you could power both the habitat and the processes for breaking the atmospheric gases down into needed items (i.e water, hydrogen as fuel, oxygen, and nitrogen). Food would likely be the only thing needed from Earth but you would basically run into that problem anywhere. As for metals, though not necessary for a colony to survive, Venus actually has a prime location for reaching the asteroid belt. Any attempt to the outer solar system uses Venus to slingshot them there. So, if you are already at Venus this makes the travel time that much quicker. Mars also isn't the best location in terms of mining for metals. Also, when a food supply chain would go to Venus they could bring more inflatable habs each time until the floating colony is large enough to begin its own agricultural harvesting. Once that is established then the food shipments would decrease in frequency significantly. Mars would need food just as often as Venus would but in this case it would be cheaper for Venus because it is much closer than Mars.

No way they could set up a habitat on the surface, but that doesn't mean they couldn't establish a habitat on Venus. Check out this article on colonizing Venus.

Hi, it has been a very long time since I last posted on this forum but I recently thought of an idea and thought this would be the best place to pitch it and see what everyone thinks. I got my inspiration from reading about Vacutrains. I was trying to think of ways to improve on it or to make it faster when it dawned on me that there is one place where you never have to worry about evacuating the environment and that was space. I then got a funny picture in my head of a giant track that went from Earth's orbit to the moon. Obviously that wouldn't work but it lead me to another idea. What if the same concept of a gauss gun or rail gun was used in space. Anyways, here is what I am picturing: A very big circular electromagnet that sits in orbit storing solar energy in very big capacitors until it is ready to be used. Then a ship needing a boost to say Mars or beyond pulls up in front of this thing. Then the circular electromagnet is turned on using a high burst of energy from the capacitors and pulls the ship through it and launches it on to its destination. To get an added boost I was thinking that maybe an asteroid or anything with a significant amount of mass could be attached to the 'gun.' I also came up with some variations on the concept like something similar to an ion engine where the two objects are initially attracted and then once the ship passes a threshold they would repel each other. Another idea I had was to use multiple donut shaped electromagnets that would continuously increase the acceleration as the ship travels through the 'barrel.' Additionally, after the ship is launched it could deploy solar sails but that's another story. So, what do you guys think? Is it plausible/practical? Thanks for considering my idea.

Just search on the internet... your bound to find a few old tests (google is great ). Now, if anyone can answer my question.. what percentage do you approximately need to get a 5 on the AP chem test? (sorry about the thread hijack).

That's what I thought... the lab is not making sense at all. Thanks for the links though, maybe I can argue it a little with my chemistry teacher :\. Would Ka be twice the H+ concentration though?

We have an unkown acid (we think its acetic) and a rough idea of the procedure goes like so... dissolve acid into 50ml of water, take 25ml and then titrate until the indicator turns pink... then add the rest of the 25 ml (untitrated) to the titrated acid. then take the pH of the new solution. Anyways, according to our lab, pKa is supposed to equal pH. I cannot figure out at all why pKa = pH. That would mean Ka = H+. One of our questions is to answer why pH = pKa and I don't think it should. If anyone has any idea I would appreciate it very much. (haven't posted in awhile... been really busy ) Edit: my bad wrong forum

Manufactured Diamonds A small company, Apollo Diamond, is making larger, industrialized diamonds and might be able to produce them in quantity and with quality. The article talks about the limitless ideas that could come from the diamonds that were never attempted before because of its rarity... and of course De Beers is complaining.

Thanks

http://chemistry.about.com/library/weekly/blbondenergies.htm try google for more

I think he's right, this blinking thing is getting out of control. It could lead to much worse things like an increased number of sniffles or even worse... throat clearings!

Yeah its in PPM, Evangelists take samples of the air and find the heathen to believer ratio. And the greater the homosexuality index the worse weather feels , kinda like with humidity and how it feels hotter.

^what I meant

collapses or explodes?