Help prove this inequality with the ceil function

[ebon sandal]

you can prove that ceil(sqrt(n))-1 <= sqrt(n-1)

[potent sedge]

Solved

Post marked as solved by @torpid scroll.

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[torpid scroll]

How could I prove this?

[rare warren]

Tip: prove that ceil(sqrt(n)) <= floor(sqrt(n)) + 1

After that the original task is trivial

[torpid scroll]

I don't understand how to continue 😦

[rare warren]

Try expressing x as floor(x) + {x}

{x} is the remainder of x modulo 1, if you will

[torpid scroll]

Is it ok this way? I thank you very much for your help 🙂 ❤️

[torpid scroll]

.solved