LIMITS AND THE GREATEST INTEGER FUNCTION

Front

What is the Greatest Integer Function?

Back

The Greatest Integer Function, denoted as ⌊x⌋, is a function that maps a real number x to the largest integer less than or equal to x.

Front

What does the notation ⌊x⌋ represent?

Back

The notation ⌊x⌋ represents the Greatest Integer Function, which returns the greatest integer less than or equal to x.

Front

How does the Greatest Integer Function behave at integer values?

Back

At integer values, the Greatest Integer Function returns the integer itself. For example, ⌊3⌋ = 3.

Front

What is the value of ⌊2.7⌋?

Back

The value of ⌊2.7⌋ is 2, as it is the largest integer less than 2.7.

Front

What is the value of ⌊-1.5⌋?

Back

The value of ⌊-1.5⌋ is -2, as it is the largest integer less than -1.5.

Front

What is the limit of the Greatest Integer Function as x approaches an integer from the left?

Back

As x approaches an integer n from the left, the limit of the Greatest Integer Function ⌊x⌋ is n-1.

Front

What is the limit of the Greatest Integer Function as x approaches an integer from the right?

Back

As x approaches an integer n from the right, the limit of the Greatest Integer Function ⌊x⌋ is n.

Front

How can the Greatest Integer Function be represented graphically?

Back

The Greatest Integer Function can be represented as a step function, where each step corresponds to an integer value.

Front

What is the domain of the Greatest Integer Function?

Back

The domain of the Greatest Integer Function is all real numbers, ℝ.

Front

What is the range of the Greatest Integer Function?

Back

The range of the Greatest Integer Function is all integers, ℤ.