When you take over one of the world's most successful companies, you don't have to promise improvement, just stability. That's the takeaway from an internal company e-mail by Tim Cook, the successor to Apple CEO Steve Jobs who resigned yesterday. The letter, sent this morning and obtained by Ars Technica, promises that "Apple is not going to change" and that taking over for Jobs is "the privilege of a lifetime." Here's the full letter by Apple's former chief operating officer:

Team:

I am looking forward to the amazing opportunity of serving as CEO of the most innovative company in the world. Joining Apple was the best decision I've ever made and it's been the privilege of a lifetime to work for Apple and Steve for over 13 years. I share Steve's optimism for Apple's bright future.

Steve has been an incredible leader and mentor to me, as well as to the entire executive team and our amazing employees. We are really looking forward to Steve's ongoing guidance and inspiration as our Chairman.

I want you to be confident that Apple is not going to change. I cherish and celebrate Apple's unique principles and values. Steve built a company and culture that is unlike any other in the world and we are going to stay true to that—it is in our DNA. We are going to continue to make the best products in the world that delight our customers and make our employees incredibly proud of what they do.

I love Apple and I am looking forward to diving into my new role. All of the incredible support from the Board, the executive team and many of you has been inspiring. I am confident our best years lie ahead of us and that together we will continue to make Apple the magical place that it is.

Tim