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The president said authorities might never understand what motivated the gunman.

“We may never understand what leads anybody to terrorize their fellow human beings like this,” Mr. Obama said. But he added, “we do know what makes life worth living.”

“What matters at the end of the day is not the small things,” he said. “It’s not the trivial things, which so often consume us in our daily lives. Ultimately it’s how we choose to treat one another and how we love one another.”

Mr. Obama, who said he had spoken with both Colorado Gov. John Hickenlooper and Aurora Mayor Steve Hogan by phone during the morning, then departed for Washington.

David Hill contributed to this report.