Cluster Limits
1. The problem asks to show clusters from lower limits to highest limits, which typically involves understanding ranges or intervals in data or functions.
2. To analyze clusters, we first identify the lower and upper limits of each cluster or interval.
3. The formula or concept used depends on the context, but generally, a cluster can be represented as an interval $$[a,b]$$ where $a$ is the lower limit and $b$ is the upper limit.
4. Important rules include that the lower limit $a$ must be less than or equal to the upper limit $b$, and clusters should not overlap if they are distinct.
5. For example, if clusters are given as intervals: $$[1,5], [6,10], [11,15]$$, these are ordered from lowest to highest limits.
6. To show clusters from lower to higher limits, list them in ascending order based on their lower limits.
7. If you have data points, you can group them into clusters by defining these intervals and then sorting the intervals.
8. Without specific data or function, the general approach is to identify each cluster's lower and upper bounds and arrange them in increasing order of their lower bounds.
9. This method helps in visualizing or analyzing data ranges or function domains effectively.
10. If you provide specific clusters or data, I can help organize or analyze them accordingly.