On October 5, 2011, Apple co-founder Steve Jobs lost his battle with pancreatic cancer at the age of 56.

Tim Cook, who took over as Apple's chief when the ailing Jobs stepped down from the position in August 2011, posted a letter of remembrance to the Apple website, in honor of Jobs' life.

Writes Cook:

Steve's passing one year ago today was a sad and difficult time for all of us. I hope that today everyone will reflect on his extraordinary life and the many ways he made the world a better place.

One of the greatest gifts Steve gave to the world is Apple. No company has ever inspired such creativity or set such high standards for itself. Our values originated from Steve and his spirit will forever be the foundation of Apple. We share the same privilege and responsibility of carrying his legacy into the future.

I'm incredibly proud of the work we are doing, delivering products that our customers love and dreaming up new ones that will delight them down the road.

It's a wonderful tribute to Steve's memory and everything he stood for.

According to 9to5Mac, the company also sent around an email with a similarly worded message to Apple employees.

The landing page for Apple.com is also featuring a video (seen above) that pays homage to Jobs, highlighting some of his most memorable moments and creations, including Macintosh computers, the iPod and the iPhone. The clip ends with the phrase "Remembering Steve" before fading into black. (Mashable notes that the video on Apple's site doesn't appear to work in the Firefox browser.)

Jobs co-founded Apple in 1976 with Steve Wozniak and Ronald Wayne. He was ousted from the company in the 1980s, but later returned to work for Apple in 1996 where he remained until his death. In the years between, he founded NeXT Computer and purchased The Graphics Group, which later became Pixar.

One day prior to his death in 2011, the iPhone 4S was unveiled -- but the innovative Apple CEO was unable to attend the event, and has since been a missed presence in the tech world. Jobs' sudden death resonated deeply with Apple fans and gadget lovers, many of whom set up shrines outside Apple Stores around the globe.

Jobs' biological sister Mona Simpson gave a stirring eulogy at her brother's funeral, revealing the visionary's last words were, "OH WOW. OH WOW. OH WOW," as he gazed past the family members who had come to his side in the final hours. Jobs' official cause of death was respiratory arrest brought on by complications with a metastatic pancreas neuroendocrine tumor.

How do you plan on remembering the former Apple CEO today? Let us know in the comments section, or tweet us at [@HuffPostTech] with your reactions. To see the original story from Steve Jobs' passing in 2011, click here. You can also check out the 10 most iconic products from Apple (here) or flip through Job's 11 best quotes (below).

Also on HuffPost:

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  • "We've never worried about numbers. In the market place, Apple is trying to focus the spotlight on products, because products really make a difference. [...] Ad campaigns are necessary for competition; IBM's ads are everywhere. But good PR educates people; that's all it is. You can't con people in this business. The products speak for themselves." <a href="http://www.huffingtonpost.com/2010/11/22/steve-jobs-1985-interview_n_787023.html#s188334&title=On_How_Computers" target="_hplink">-- Playboy interview, 1985</a>

  • "That's been one of my mantras -- focus and simplicity. Simple can be harder than complex: You have to work hard to get your thinking clean to make it simple. But it's worth it in the end because once you get there, you can move mountains." -- <a href="http://www.businessweek.com/bwdaily/dnflash/may1998/nf80512d.htm" target="_hplink">BusinessWeek interview, May 1998 </a>

  • "The most compelling reason for most people to buy a computer for the home will be to link it into a nationwide communications network. We're just in the beginning stages of what will be a truly remarkable breakthrough for most people--as remarkable as the telephone." <a href="http://www.huffingtonpost.com/2010/11/22/steve-jobs-1985-interview_n_787023.html#s188334&title=On_How_Computers" target="_hplink">-- Playboy interview, 1985</a>

  • "We've kept our marriage secret for over a decade." -- Jobs' answer to Kara Swisher asking about the "greatest misunderstanding" in Jobs' relationship with Bill Gates. (<a href="http://allthingsd.com/20070531/d5-gates-jobs-transcript/" target="_hplink">May 2007</a>)

  • "It's really hard to design products by focus groups. A lot of times, people don't know what they want until you show it to them." -- <a href="http://www.businessweek.com/bwdaily/dnflash/may1998/nf80512d.htm" target="_hplink">BusinessWeek interview, May 1998 </a>

  • "Picasso had a saying: 'Good artists copy, great artists steal.' We have always been shameless about stealing great ideas...I think part of what made the Macintosh great was that the people working on it were musicians, poets, artists, zoologists and historians who also happened to be the best computer scientists in the world." --<a href="http://www.youtube.com/watch?v=CW0DUg63lqU" target="_hplink"> 1994</a>

  • "[Y]ou can't connect the dots looking forward; you can only connect them looking backwards. So you have to trust that the dots will somehow connect in your future. You have to trust in something -- your gut, destiny, life, karma, whatever. This approach has never let me down, and it has made all the difference in my life." <a href="http://news.stanford.edu/news/2005/june15/jobs-061505.html" target="_hplink">-- Stanford University commencement address, June 2005.</a>

  • "My sex life is pretty good these days, Walt. How's yours?" -- Jobs's response to a question from Walt Mossberg about how Jobs feels about Google and if he feels "betrayed." <a href="http://www.huffingtonpost.com/2010/06/02/steve-jobs-all-things-dig_n_597818.html#s95757&title=On_Sex_And" target="_hplink"> (June, 2010)</a> (Jobs also added, "Well they decided to compete with us. We didn't go into the search business.")

  • "Remembering that I'll be dead soon is the most important tool I've ever encountered to help me make the big choices in life. Because almost everything -- all external expectations, all pride, all fear of embarrassment or failure - these things just fall away in the face of death, leaving only what is truly important. Remembering that you are going to die is the best way I know to avoid the trap of thinking you have something to lose. You are already naked. There is no reason not to follow your heart. ... Stay hungry. Stay foolish." <a href="http://news.stanford.edu/news/2005/june15/jobs-061505.html" target="_hplink">-- Stanford University commencement address, June 2005.</a>

  • "I read a study that measured the efficiency of locomotion for various species on the planet. The condor used the least energy to move a kilometer. Humans came in with a rather unimpressive showing about a third of the way down the list....That didn't look so good, but then someone at Scientific American had the insight to test the efficiency of lomotion for a man on a bicycle and a man on a bicycle blew the condor away. That's what a computer is to me: the computer is the most remarkable tool that we've ever come up with. It's the equivalent of a bicycle for our minds." <a href="http://www.mlfilms.com/productions/m_and_i" target="_hplink">-- Interview for the documentary "Memory and Imagination," 1990</a>

  • "My model for business is The Beatles. They were four guys who kept each other's kind of negative tendencies in check. They balanced each other and the total was greater than the sum of the parts. That's how I see business: great things in business are never done by one person, they're done by a team of people." <a href="http://www.cbsnews.com/video/watch/?id=4835857n" target="_hplink">-- Interview with 60 Minutes, 2003</a>