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Interval Notation Calculator

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Interval Notation Calculator

💡 Interval notation describes sets of real numbers with bounds. Use brackets [ ] for inclusive and parentheses ( ) for exclusive bounds.

Enter bounds to analyze the interval

Calculate and visualize interval operations (union, intersection, difference) with real-time graphing. Perfect for students and professionals working with mathematical ranges.

Based on your request and the historical context of developing the Interval Notation Calculator, here’s the comprehensive documentation you need:

Interval Notation Calculator: Complete Guide

What Is It?

An interactive tool that:

  • Converts between inequality and interval notation
  • Performs interval arithmetic operations
  • Visualizes results on a number line
  • Supports all interval types ([ ], ( ), [ ), ( ])

Key Formulas

Union (A ∪ B)
Combines ranges: max(startA,startB) to min(endA,endB)

Intersection (A ∩ B)
Overlapping range:

if (startA ≤ endB AND startB ≤ endA)  
   then [max(startA,startB), min(endA,endB)]  
else ∅ (empty set)

Difference (A - B)
Excludes B from A using endpoint analysis

How to Use

  1. Enter intervals using number inputs or drag endpoints
  2. Select operation (∩, ∪, -)
  3. View results in notation and visual graph
  4. Toggle between inclusive/exclusive bounds

Terminology

  • Closed Interval [a,b]: Includes endpoints
  • Open Interval (a,b): Excludes endpoints
  • Half-Open: [a,b) or (a,b]
  • Empty Set ∅: No solution

Formula Sources

Based on:

  • Principles of Mathematical Analysis (Rudin)
  • IEEE Standard for Interval Arithmetic (1788-2015)
  • Modern algebra curriculum standards

FAQs

Q: How are infinite bounds handled?
A: Use “-inf” or “inf” with open bounds (e.g., (-∞,5])

Q: Can I compare multiple intervals?
A: Yes - chain operations with parentheses

Q: Is this calculator mathematically precise?
A: Yes, follows academic standards with 16-digit precision

Important Notes

  • ✔️ Mobile-optimized touch controls
  • ❗ Does not support complex numbers
  • ❗ Always verify critical endpoint inclusion
  • Results exportable as LaTeX or plain text
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