This tool helps you convert inequalities into interval notation effortlessly.

## How to Use the Interval Notation Calculator

To use this calculator, enter the intervals in the prescribed format. Each interval should be in the form `[a,b]`

or `(a,b)`

where a and b are numbers. Use the `[`

and `]`

brackets for inclusive intervals, and `(`

and `)`

for exclusive intervals. Select the desired operation (Union or Intersection) and click “Calculate”.

### Explanation of Calculations

The Union operation finds the combined range of both intervals, while the Intersection operation finds the overlapping range. Both operations take into account whether the endpoints are inclusive or exclusive.

### Limitations

This calculator currently supports only two intervals at a time and simple union and intersection operations. Ensure the input format is correct to avoid errors.

## Use Cases for This Calculator

### Calculating Union of Two Intervals

Calculate the union of two intervals by inputting their start and end points. The calculator will give you the combined interval in simplified notation. Easily compare overlapping intervals with this feature.

### Determining Intersection of Two Intervals

Find the intersection of two intervals by entering their respective start and end values. The calculator will return the shared interval, simplifying your analysis and helping you identify common ranges.

### Checking for Empty Intersection

Determine if two intervals have an empty intersection by inputting their values. The calculator will inform you if there is no overlap between the intervals, offering quick insights into the relationship between the ranges.

### Calculating Complement of an Interval

Calculate the complement of an interval by providing its start and end points. The calculator will display the range outside the specified interval, aiding in set operations and making it easier to work with complements.

### Combining Multiple Intervals

Combine multiple intervals by entering their start and end values. The calculator will merge the intervals into a simplified notation, allowing you to work with multiple ranges at once and streamline your calculations.

### Calculating the Relative Complement

Determine the relative complement of one interval with respect to another. Input the intervals, and the calculator will display the range of values in the first interval that do not overlap with the second, assisting you in set theory operations.

### Finding the Symmetric Difference

Find the symmetric difference between two intervals by inputting their start and end points. The calculator will show the range of values that are exclusive to each interval, aiding in your understanding of the differences between sets.

### Checking for Subset Relation

Determine if one interval is a subset of another by entering their values. The calculator will indicate if the first interval lies entirely within the second, helping you establish containment relationships between ranges.

### Calculating the Cartesian Product of Two Intervals

Calculate the Cartesian product of two intervals by inputting their start and end values. The calculator will display the pairs of values from each interval, facilitating your work in combinatorics and set theory with ease.

### Converting Between Interval Notations

Convert between different interval notations (closed, open, half-open) by entering the interval values. The calculator will transform the notation to your preferred format, simplifying your representation of ranges and enhancing clarity in your calculations.