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A Cinderella like tale in which Olive is the princess and Popeye is the prince. Bluto is the shopowner brute who bullies Olive, only to get taught a lesson by a buff, spinach-eating Prince Popeye. Animation by Al Eugster and William B. Pattengill, story by Irving Spector, scenics by Robert Connavale, and music by Winston Sharples. Produced in 1952. Public Domain.

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∑_{k=1 → ∞} 1/k = ∏_{prime p} 1 / [1 − 1/p]

For a better pic:

http://www.forkosh.dreamhost.com/mimetex.cgi?\sum_{k=1}^{\infty}\frac{1}{k}=\prod_{p}^{}\frac{1}{1-\frac{1}{p}}

Okay… I already do understand the proof to this equality. I admit that they are equal, and I understand how its proven, etc, etc.

But this is my question…

Term for term, these two are never equal… they only become equal at the infinitieth k and at the infinitieth prime. Until then, no term in the sequences equal. And they in fact grow at different rates… So for no finite point are they equal, or growing at the same rate, or anything.

They only equal when the infinite series and infinite products have been “evaluated”.

BUT… the infinite sum diverges… and so does the infinite product. They DIVERGE. So even AT the infinite point in their sequence, how can we still say they are equal?

I just have a hard time conceptualizing their equality considering that they diverge and are never equal along their journey to divergence.

Is this an example of divergent “infinities” being equal? Can one side minus the other side equal ∞ – ∞ = 0 ?
Sean H… you dont seem to understand. Just because two expressions diverge does not mean they can be set equal to one another. No two divergent statements are equal just because they both diverge. Their equality is proven. But the divergence makes that equality meaningless
I swear to God… whatever moron up thumbed Sean H for the total BS answer… dont even waste your time ever looking at my questions again.

I am trying to develop a small shopping website, and I am trying to find the best host for me. I want the website to include the following:

1- Customer login.
2- Customer Signup/Registration.
3- Pictures of all the collection.
4- Shopping cart.

In the future, I might want to add the following:
1- Live chat.
2- Email.
3- Advertisements.
4- An inventory of all the items.
5- Order status.
6- Email notification send to customer.
7- Search engine to search within the website.
8- customer feed back, more like placing a comment area.
9- A wishlist.

Which webhost do you think can best fullfill my needs? Note, I know how to build a website from scratch. However, I do need some tools to assist me, such as, having a database to store customer info in, products, and so forth. Email service provider and how to create it. I also need free ads on Google and Yahoo, and perhaps facebook?

I have checked sitebuild it and bluehost. I liked sitebuild it but I don’t think it supports having different websites. I have to pay for every website individually. I also think that bluehost is too expensive, and that’s why I didn’t like it.

Please help.

Thanks a lot!

Game Center sparks light reactions from competing iPhone social network devs
Yesterday, Apple announced Game Center , a social gaming service for iPhone. Pretty much everyone with an iPhone has reason to be delighted with this development, except for companies like OpenFeint and ngmoco , which already operate social network gaming services for iPhone in OpenFeint and Plus+, respectively. Are both companies freaking out? Not in public. In a statement , OpenFeint …

Read more on Joystiq

It seemed somewhat unexpected that McCain would choose a VP who have more experience catching fish than dealing with foreign policy or national affairs, especially when there were other experienced VPs. Was this the right movie or did he shoot himself in the foot trying to make a headline splash?

Academy Award winning actor James Earl Jones performs from Shakespeares Othello at the White House Evening of Poetry, Music, and the Spoken Word on May 12, 2009. (public domain)