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Eckels goes to the time machine business so he could go back in time to shoot animals and metions that he is not happy that Keith won presidency.
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All of the characters are told to stay on the path that they are supposed to so that they don't alter the future.
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They go back millions of years so that they could go safari hunting.
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Travis tells them how infinitesimally can occur if they change one thing in the past.
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Eckels runs off of the path and Travis is afraid that he has changed the future.
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He does this because he is afriad that the business is going to lose a lot of money.
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He makes him do this because bullets were not there in that time period, also to try to prevent the future from being changed.
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They all go back to the present hoping that nothing has changed.
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They can tell this from how the president is different and how the way the words on the sign are different.
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He points the gun to his head and then a "sound of thunder" goes off. He kills him because he was the reason that the future was altered.