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Short Answer Prove the statement For any real number x, [[x]]=[x] TTT Arial 3 (12pt) - T - = - = - S es Path:p Words:0 QUESTIFor the functions below, indicate whether the function is: Onto One-to-one Bijection. Example Onto not the function is onto.

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Answer #1

Let us define ceil(x)=x+p where p=difference between smallest integer greater than x and x

So,

ceil(ceil(x))=ceil(x+p)=x+p+k where k is integer between the smallest integer greater than x+p and x+p

Since x+p is itself an integer so, k=0

So,

ceil(ceil(x))=x+p

where x+p is ceil(x)

So,

ceil(ceil(x))=ceil(x)

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