The largest integer in this interval is \( x = 3 \).

Wed, 06 May 2026 17:57:56 +0000

# The Largest Integer in This Interval is \( x = 3 \) When working with intervals of numbers, identifying the largest integer within a given range is essential in many mathematical and computational applications. In the case of a simple interval, the largest integer \( x \) satisfies the condition of being the greatest whole number less than or equal to the upper bound of the interval. For example, consider the closed interval from \( a \) to \( b \), inclusive: \([a, b]\). The largest integer \( x \) within this range is formally defined as: \[
x = \lfloor b \rfloor
\]
where \( \lfloor \cdot \rfloor \) denotes the floor function, which returns the greatest integer less than or equal to the given number. Now, consider the specific interval in question — a well-defined range used to illustrate this concept. The largest integer in this interval is clearly \( x = 3 \), indicating that the upper bound of the interval is greater than or equal to 3 but less than 4. Formally, we find: