Timothy "Tim" Cook said Steve Jobs’s work will live on at Apple. (Tony Avelar/BLOOMBERG)

Tim Cook, Apple’s new chief executive, wrote what was likely one of the most difficult memos of his life Wednesday night to tell all Apple employees that co-founder Steve Jobs had died.

“Apple has lost a visionary and creative genius, and the world has lost an amazing human being,” Cook wrote. “No words can adequately express our sadness at Steve’s death or our gratitude for the opportunity to work with him. We will honor his memory by dedicating ourselves to continuing the work he loved so much.”

A statement on the company’s Web site said that Jobs “spirit will forever be the foundation of Apple.”

Cook, who has been Apple’s top executive for just over a month, has said repeatedly that he is dedicated to keeping the company the same as it was under Jobs.

As head of Apple, Cook faces an increasingly competitive technology market. Google, Amazon, Facebook and others are moving to take over the areas of consumer technology where Apple has had the first advantage.

But the company appears to have a solid plan in place, taking pains at Tuesday’s iPhone 4S event in California to showcase not only Cook but the stable of Apple veterans working with him. Apple has also been jumping into the growing market in Asia and committing heavily to hot technologies such as cloud computing.

Tech analysts Shaw Wu of Sterne Agee said that Jobs’s legacy will definitely live on at the company he founded with Steve Wozniak in 1976 and built into an empire, comparing Jobs to Walt Disney and Thomas Edison.

“It is the culture of innovation, thinking different, risk taking and execution that will live on,” Wu said.

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