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I notice that I can do things like 2 << 5 to get 64 and 1000 >> 2 to get 250.

Also I can use >> in print:

print >>obj, "Hello world"

What is happening here?

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I think it is important question and it is not answered yet (the OP seems to already know about shift operators). Let me try to answer, the >> operator in your example is used for two different purposes. In c++ terms this operator is overloaded. In the first example it is used as bitwise operator (left shift), while in the second scenario it is merely used as output redirection. i.e.

2 << 5 # shift to left by 5 bits
2 >> 5 # shift to right by 5 bits
print >> obj, "Hello world" # redirect the output to obj, 

example

with open('foo.txt', 'w') as obj:
    print >> obj, "Hello world" # hello world now saved in foo.txt

update:

In python 3 it is possible to give the file argument directly as follows:

print("Hello world", file=open("foo.txt", "a")) # hello world now saved in foo.txt

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