How can i prove the following?
for any integer n>=1,
{celling of [lg(n+1)]} = (floor of lg n) + 1
thanks for the help

reinsuranc

Hi. I understand induction, but I am confused.

Is lg supposed to be logarithm?

What is celling? Is this supposed to be ceiling?

What do ceiling and floor have to do with logarithms?

Maybe you can restate this problem.

CroCivic91

"lg x" is short for "logarithm of x with the base 2".

"Celling" should indeed be "ceiling". "Ceiling" is a function that takes a real number and returns an integer, in the following rule:

ceiling( x ) = min{ n : n >= x & n is an integer }
For example, ceiling( pi ) = 4, ceiling( -pi ) = -3

"Floor" is a function defined as:

floor( x ) = max{ n : n <= x & n is an integer }
For example, floor( pi ) = 3, floor( -pi ) = -4

Of course, floor( 3 ) = 3, and ceiling( 3 ) = 3.