Time travel is fiction, unless you are referring to traveling ahead in time at the rate one one minute per minute. As fiction, you can do pretty much what you want with temporal displacement, so science fiction stories treat that ability in many different ways.
What causes a paradox doesn't necessarily cause a paradox in a different story. Our friends at Minute Physics gives us an overview of how time travel varies between stories. -via Geeks Are Sexy
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... and not very spoiler.
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