High Cap value of ⌈3.02⌉

Question

I was in a dilemma on finding out the value of ⌈3.02⌉.

From one of the teaching staff I got to know that ⌈3.02⌉ is 4.... Even if it is ⌈1.0001⌉ also it is 2.

But from the other teaching staff I got to know that ⌈3.02⌉ is 3.

I don't know which one is correct.

Can anyone from here clarify my doubt please.

Thanks

Answer 1

By definition, the ceiling function of $x$ is defined as

The smallest integer $n$ such that $n\geq x$.

So, let's see what that definition means for $x=3.02$. Can $\lceil x \rceil = 3$? Well, that would mean that $3\geq3.02$, but that is clearly not true.

So, $\lceil x \rceil $ must be $4$ or more. Can it be $4$?

• Is $4\geq 3.02$? yes.
• Is $4$ the smallest such number? yes, because any smaller number would be smaller than or equal to $3$, so it would be smaller than $3.02$.