Under what conditions is \lfloor x\rfloor=\lceil x\rceil-1

sanuluy

sanuluy

Answered question

2021-08-03

Under what conditions is x=x1

Answer & Explanation

Delorenzoz

Delorenzoz

Skilled2021-08-04Added 91 answers

First, explain how the floor and ceiling work.
The definition of a floor function is a function that takes an input of x and returns the biggest integer less than or equal to x as the output.
A function known as a ceiling function produces the lowest integer larger than or equal to x from an input of x.
Use both functions as examples to define now.
example of floor function: 
2.3=2 
example of ceiling function: 
2.3=3 
Consider the case of integers. 
let x=3 
3=3 
3=3 
but 3q31 that is 3q2 , this statement is not true for integers. 

Сonsider the case of real numbers other than integers. 
First take case of the positive real fraction numbers. 
let x=2.3 
2.3=2 
2.3=3 
but 2=31 that is 2=2 
so, this statement is true for positive real fraction. 
Еake case of negative real fraction numbers. 
let x=2.3 
2.3=3 
2.3=2 
but 3=21 that is 3=3 , this statement is true for negative real fraction. 

The statement is true for all real numbers except integers. So, 
RZ

Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-14Added 2605 answers

Answer is given below (on video)

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