Final answer:
To prove that if x is a real number, then floor(floor(x/2)/2) = floor(x/4), we can use the properties of the floor function.
Step-by-step explanation:
To prove that if x is a real number, then floor(floor(x/2)/2) = floor(x/4), we can use the properties of the floor function.
Let's consider an arbitrary real number x. Dividing x by 2 gives us floor(x/2) as a result, which represents the greatest integer that is less than or equal to x/2.
Dividing floor(x/2) by 2 gives us floor(floor(x/2)/2), which represents the greatest integer that is less than or equal to floor(x/2)/2.
On the other hand, dividing x by 4 gives us floor(x/4), which represents the greatest integer that is less than or equal to x/4.
Since the floor function rounds down to the nearest integer, floor(x/4) will always be less than or equal to floor(floor(x/2)/2), making the given statement true for any real number x.