Step Functions Answers
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1
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Is the statement true for all real numbers? Explain.
Answer:
The statement is not true for all real numbers. It is only true for non-integer (decimal or fractional) values of x. If x is an integer, the ceiling function ⌈x⌉ equals x, but the floor function ⌊x + 1⌋ equals x + 1. Since x does not equal x + 1 for any integer, the equation does not hold when x is an integer.
2
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Does your answer include the following?
A
The statement is not true for all real numbers. It is only true for decimal or fractional values of x .B
If x is an integer, then the ceiling function returns x when the input is x . But, the flooring function returns x + 1 when the input is x + 1.C
Since x does not equal x + 1 when x is an integer, the expressions are not equal when x is an integer.Did you find these answers helpful?
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