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The boxer had been suffering from a respiratory illness, a condition that was complicated by Parkinson's disease.
"I am happy my father no longer struggles. He is in a better place. God is the greatest," his daughter Maryum said on Saturday.
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Ali's body is being returned in the next two days to his hometown of Louisville, Kentucky, where his funeral is scheduled for Friday afternoon at the KFC Yum! Center. The celebration of his life will feature a funeral procession through the town and public celebration. The boxer will be buried in a private service at the city's Cave Hill Cemetery.
The service will be presided over by an imam and feature eulogies by former President Bill Clinton, sports journalist Bryant Gumber and actor Billy Crystal.
Rahaman Ali stood in a little house on Grand Avenue and dabbed his eyes as he shook hand after hand.
The visitors had come from as far away as Georgia and as near as down the street. They came despite the pouring rain to pay tribute to his brother, The Greatest, Muhammad Ali.
"God bless you all," the 72-year-old Rahaman said to each.
NEW: Muhammad Ali funeral to be held in Louisville Friday at 2 p.m.; President Bill Clinton, Billy Crystal, Bryant Gumbel to give eulogies— ABC News (@ABC) June 4, 2016
As the world mourned Muhammad Ali, his death held special meaning here in Louisville, where the boxing great was the city's favorite son.
"He was one of the most honorable, kindest men to live on this planet," his brother said while greeting mourners at their childhood home, recently renovated and turned into a museum.
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Cars lined both sides of the street for blocks. The guests piled flowers and boxing gloves around the marker designating it a historical site. They were young and old, black and white, friends and fans.
Another makeshift memorial grew outside the Muhammad Ali Center downtown, a museum built in tribute to Ali's core values: respect, confidence, conviction, dedication, charity, spirituality.
"Muhammad Ali belongs to the world," Louisville Mayor Greg Fischer said at a memorial service Saturday morning outside Metro Hall. "But he only has one hometown."
Rahaman recalled what Ali was like as a boy named Cassius Marcellus Clay Jr., long before he became the most famous man in the world, the Louisville Lip, celebrated as much for his grace and his words as his lightning-fast feet and knockout punch.
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In their little pink house in Louisville's west end, the brothers liked to wrestle and play cards and shoot hoops.
"He was a really sweet, kind, loving, giving, affectionate, wonderful person," Rahaman said, wearing a cap that read "Ali," the last letter formed by the silhouette of a boxer ready to pounce.
When he was 12 years old, Ali had a bicycle that was stolen and he told a police officer he wanted to "whoop" whoever took it, Fischer said at the memorial service. The officer told him he'd have to learn how to box first.
Daniel Wilson was one year behind Ali at Central High School and remembered he was so committed to his conditioning that he didn't get on the school bus like everybody else. Instead, he ran along beside it, three miles all the way to school each morning.
"The kids on the bus would be laughing and Ali would be laughing too," he recalled Saturday morning at the Grand Avenue home where he went to pay his respects to an old friend.
Ruby Hyde arrived at the memorial holding an old black-and-white framed photo of a young Ali. She'd been a water girl at his amateur bouts as a teenager in Louisville, and seen even then that there was something special, something cerebral, about the way he fought.
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Years later, he came back to the old neighborhood as a heavyweight champion, driving a Cadillac with the top down.
"All the kids jumped in and he rode them around the block," she remembered.
He never forgot where he came from, she said.
"He's done so much for Louisville. He's given us so much," said Kitt Liston, who as girl growing up in Louisville admired Ali's unblinking fight for justice and peace. "He's truly a native son. He's ours."
Liston's voice trembled as she recounted running into him at a baseball game a few years ago.
"I got to tell him how much I cared about him. He put that big ol' paw out and just shook my hand," she said. "He just had time for everybody."
The mayor ordered the city's flags flown at half-staff.
Outside Metro Hall, Fischer pointed west, toward Ali's childhood home, about three miles away in one of the city's poorest zip codes.
"There can only be one Muhammad Ali, but his journey from Grand Avenue to global icon serves as a reminder that there are young people with the potential for greatness in the houses and neighborhoods all over our city, our nation, our world," he said.
Fischer told mourners to teach all children Ali's legacy: that a kid from Kentucky can grow up to be The Greatest.
"That's how we become champions," he said. "Muhammad Ali has shown us the way."
For more on the life and legacy of Muhammad Ali, click here.
He shook up the world, and the world's better for it. Rest in peace, Champ. pic.twitter.com/z1yM3sSLH3— President Obama (@POTUS) June 4, 2016
"We pray that the greatest fighter of them all finally rests in peace." ?President Obama #RIPMuhammadAli— Barack Obama (@BarackObama) June 4, 2016
"He who is not courageous enough to take risks will accomplish nothing in life." - Muhammad Ali pic.twitter.com/X9eW0god2n— Nightline (@Nightline) June 4, 2016
"Don?t count the days; make the days count." Rest in peace, Muhammad Ali. pic.twitter.com/kCVoRadwwQ— Nightline (@Nightline) June 4, 2016