Analyze finite sets with sorted unique numeric values. View least bounds, greatest bounds, and range. Save tables as CSV or PDF for later review.
| Example Set | Sorted Set | Infimum | Supremum | Range |
|---|---|---|---|---|
| 7, 2, 9, 4 | 2, 4, 7, 9 | 2 | 9 | 7 |
| -3, -1, 5, 8 | -3, -1, 5, 8 | -3 | 8 | 11 |
| 1/2, 3/2, -1, 2 | -1, 0.5, 1.5, 2 | -1 | 2 | 3 |
For a nonempty finite set A:
inf(A) = min(A)
sup(A) = max(A)
Range = sup(A) - inf(A)
Midpoint = (inf(A) + sup(A)) / 2
The infimum is the greatest lower bound. The supremum is the least upper bound. In finite sets, both bounds are attained by actual values inside the set.
Understanding infimum and supremum helps you describe a set with precision. These two values define the tightest lower and upper bounds. In real analysis, they are basic but powerful ideas. They also appear in optimization, inequalities, statistics, and calculus.
An infimum is the greatest lower bound of a set. A supremum is the least upper bound. For a finite set of real numbers, the infimum equals the minimum. The supremum equals the maximum. That makes a finite set easier to study and verify.
This infimum and supremum calculator lets you enter comma separated values, spaces, fractions, or line breaks. It sorts the set, removes duplicates if needed, and returns the key bounds. You can also review the range and midpoint. These extra values help you inspect spread and symmetry quickly.
Students use infimum and supremum when solving inequality questions and sequence problems. Teachers use them when explaining bounded sets and completeness. Analysts use them when comparing datasets and checking edge values. A clear lower bound prevents confusion. A clear upper bound improves interpretation.
The main rule is simple. First identify every value in the set. Then order the values from smallest to largest. The smallest value is the infimum for any nonempty finite set. The largest value is the supremum for any nonempty finite set. If the set is infinite, the same ideas still apply, but the bound may not be attained.
You can also use this tool to verify homework steps. Fractions such as 3/4 and negative decimals are accepted. The sorted output helps you catch entry mistakes fast. Because the result table is structured clearly, you can compare original entries and working values without extra manual checking.
A good workflow saves time. Paste your values. Choose the precision you want. Submit the form and read the result box above it. Then export the result as CSV or PDF for notes, reports, or homework review.
This page also includes an example table, a formula section, and plain language guidance. That makes it useful for quick answers and revision. When you need exact lower and upper bounds, a focused infimum and supremum calculator can keep your work organized and reliable.
Infimum is the greatest lower bound. Supremum is the least upper bound. In finite nonempty sets, they match the minimum and maximum values.
For a finite set, yes. The smallest value is the infimum, and the largest value is the supremum.
Yes. Enter values like 1/2, -3/4, or 5/8. The calculator converts them into decimals during processing.
Duplicates do not change the infimum or supremum. They may change counts, so this page lets you remove duplicates for a cleaner working set.
No. This page is designed for nonempty finite numeric sets entered as values. Interval notation and symbolic infinite sets need separate logic.
The range equals supremum minus infimum. It shows the spread between the highest and lowest values in the working set.
CSV creates a simple spreadsheet-friendly file. PDF is useful for printing or saving a clean report for assignments, notes, or documentation.
Check for empty entries, text labels, invalid fractions, or mixed symbols. Use only numeric values separated by commas, spaces, semicolons, or line breaks.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.