1. The problem is to find the upper and lower boundaries for the number 6. 2. Upper and lower boundaries refer to the smallest and largest numbers that round to 6 under a certain rounding rule. 3. Assuming we are rounding to the nearest whole number, the lower boundary is the smallest number that rounds up to 6, and the upper boundary is the largest number that rounds down to 6. 4. For rounding to the nearest integer, numbers from $5.5$ up to but not including $6.5$ round to 6. 5. Therefore, the lower boundary is $5.5$ and the upper boundary is $6.499\ldots$ (just less than $6.5$). 6. In interval notation, the boundaries are $[5.5, 6.5)$ where $5.5$ is included and $6.5$ is excluded. 7. This means any number $x$ such that $5.5 \leq x < 6.5$ will round to 6. Final answer: Lower boundary = $5.5$, Upper boundary = $6.5$ (exclusive).