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The set builder notation {x|x is less than or equal to 4} reads as x such that x is less than or equal to 4, so we are talking about all of the numbers that are less than or equal to 4, or all numbers from negative infinity to 4, including 4...
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So the chain of inequalities can also be written as Now for each real number , the “floor-plus-one” of is the unique integer such that ; hence we can conclude that It is then straightforward to give a formula for , using the fact that the th bounce starts at time , and the ball...