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Travis the guide explains how one small error in the past can alter the events of the future, and the character Eckels disagrees and causes Travis to explain more thoroughly about how killing a mouse can cause an effect on the evolution of animals.
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The character Eckels steps of the path and without knowing it he kills a butterfly and they don't find out until they return to the future. The reason he stepped off the path was because of the fear of the Rex charging towards them covering a hundred yards a second.
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The hunters enter the time machine and travel back to the time of the Dinosaurs, while getting instructions from the guide Travis.
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It is the year 2055 and the hunters are preparing to time travel to kill a Tyrannosaurus Rex.
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When the hunters return they find that everything is off, not normal or the same as they had left it. There was still people but words were spelled differently, a different president, and Eckels realizes it is all his fault.
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Holding to his word from early in the text, if Eckels changed the future he would die, Travis raises his rifle and shoots Eckels in the back for the irreversible changes to the future caused by stepping on the butterfly.