Why does "x = x.append(...)" not work in a for loop?

I am trying to append objects to the end of a list repeatedly, like so:

list1 = []
n = 3
for i in range(0, n):
    list1 = list1.append([i])

But I get an error like: AttributeError: 'NoneType' object has no attribute 'append'. Is this because list1 starts off as an empty list? How do I fix this error?

_{This question is specifically about how to fix the problem and append to the list correctly. In the original code, the reported error occurs when using a loop because .append returns None the first time. For why None is returned (the underlying design decision), see Why do these list operations return None, rather than the resulting list?.}

_{If you have an IndexError from trying to assign to an index just past the end of a list - that doesn't work; you need the .append method instead. For more information, see Why does this iterative list-growing code give IndexError: list assignment index out of range? How can I repeatedly add elements to a list?.}

_{If you want to append the same value multiple times, see Python: Append item to list N times.}