String Comparison, Ordering & Equality

Consider this deceptively simple question: Is 'Apple' equal to 'apple'?

Your intuition says yes—they're clearly the same word. But to a computer, depending on the comparison method used, they might be completely different strings, as unrelated as 'Apple' and 'Zebra'.

This is the domain of case sensitivity—one of the most common sources of bugs in string processing. Users type 'HELP' when your system expects 'help'. A database query for 'John' misses entries spelled 'john'. A password comparison fails because the login form auto-capitalized the first letter.

Understanding case sensitivity deeply means knowing:

• Why computers treat uppercase and lowercase differently
• When case-sensitive comparison is appropriate
• When case-insensitive comparison is needed
• How to implement case-insensitive operations correctly
• The surprising edge cases that break naive implementations

Case sensitivity isn't a design flaw—it's a direct consequence of how characters are represented in computers.

Historical Context:

When ASCII was designed in the 1960s, each character needed a unique numeric code. Rather than treating 'A' and 'a' as the same character with different rendering, they were assigned completely different codes:

• 'A' → 65

• 'B' → 66

• ...

• 'Z' → 90

• 'a' → 97

• 'b' → 98

• ...

• 'z' → 122

This wasn't arbitrary—the 32-value gap between uppercase and lowercase was deliberate, making case conversion a simple bit manipulation.

The Technical Reality:

To a computer comparing bytes:

• 'A' (65) and 'a' (97) are as different as '!' (33) and 'p' (112)
• String comparison sees completely different byte sequences
• There's no inherent concept of 'same letter, different case'

Lexicographical Consequence:

Since uppercase letters have lower ASCII values than lowercase letters:

• 'Z' (90) < 'a' (97)
• All uppercase letters come before all lowercase letters in ASCII order
• "Zebra" < "apple" lexicographically

This ordering often surprises developers expecting 'alphabetical' order where 'a' (regardless of case) comes before 'b' (regardless of case).

Why Preserve Case Distinction?

You might wonder: why not just treat 'A' and 'a' as identical? The answer is that case often carries meaning:

• Identifiers: In many languages, MyClass and myclass are different identifiers
• Proper nouns: "Paris" (city) vs "paris" (rarely used without context)
• Acronyms: "AIDS" vs "aids" (helping vs the disease)
• Formatting: Preserving user input case matters for display
• Passwords: Case is often significant for security

Case sensitivity is the default because it preserves information. Case insensitivity discards information.

Case sensitivity affects virtually every string operation. Let's catalog where it appears:

1. Equality Comparison:

The most direct case:

"Apple" == "apple"  →  false (case-sensitive)
"Apple" == "Apple"  →  true

Most programming languages default to case-sensitive equality.

2. Lexicographical Ordering:

As discussed in the previous page, case affects sort order:

Sorted: ["Apple", "Banana", "apple", "banana"]
// Uppercase words come first because 'B' (66) < 'a' (97)

3. Searching and Pattern Matching:

"Hello World".contains("hello")  →  false (typically)
"Hello World".indexOf("WORLD")   →  -1 (typically)

Search operations are usually case-sensitive by default.

4. Regular Expressions:

Regex matching is case-sensitive unless you use flags:

/hello/.test("Hello")  →  false
/hello/i.test("Hello") →  true (with case-insensitive flag)

5. Hash Tables and Dictionaries:

Hash functions treat different byte sequences as different keys:

map["Apple"] = 1
map["apple"] = 2
// These are two different keys!
map.get("Apple")  →  1
map.get("apple")  →  2

6. Database Queries:

SQL behavior varies by database and collation:

-- In MySQL with default collation (often case-insensitive)
SELECT * FROM users WHERE name = 'John'  
-- May match 'JOHN', 'john', 'John'

-- In PostgreSQL (case-sensitive by default)
SELECT * FROM users WHERE name = 'John'
-- Only matches exactly 'John'

7. File Systems:

• Windows/macOS (default): Case-preserving but case-insensitive
  • File.txt and file.txt are the same file
• Linux: Case-sensitive
  • File.txt and file.txt are different files

When you need case-insensitive comparison, there are several approaches:

Strategy 1: Convert Both Strings to Same Case

The most common approach—convert both strings to lowercase (or uppercase) before comparing:

function equalsIgnoreCase(a, b):
    return a.toLowerCase() == b.toLowerCase()

Pros:

• Simple to understand and implement
• Works for equality, contains, startsWith, etc.

Cons:

• Creates temporary string objects (memory overhead)
• May not handle all languages correctly (locale issues)
• Case conversion itself can be expensive for long strings

Strategy 2: Library Functions for Case-Insensitive Comparison

Many languages provide built-in case-insensitive comparison:

// JavaScript
"Apple".localeCompare("apple", undefined, { sensitivity: 'accent' })

// Python
"Apple".casefold() == "apple".casefold()  // casefold is more aggressive than lower

// Java
"Apple".equalsIgnoreCase("apple")

// C#
string.Equals("Apple", "apple", StringComparison.OrdinalIgnoreCase)

Pros:

• Often more efficient (can compare in-place)
• Handles locale-specific cases correctly
• Clear intent in code

Cons:

• API varies by language
• May still create internal temporary objects

Strategy 3: Case-Insensitive Data Structures

Some scenarios need case-insensitive storage:

# Python: Case-insensitive dictionary with custom key
class CaseInsensitiveDict:
    def __init__(self):
        self._data = {}
    
    def __setitem__(self, key, value):
        self._data[key.lower()] = (key, value)  # Store original key
    
    def __getitem__(self, key):
        return self._data[key.lower()][1]

This approach normalizes at storage time, avoiding repeated conversions at lookup time.

Here's a fascinating case sensitivity bug that has plagued software for decades: The Turkish I Problem.

The Issue:

In English and most European languages:

• 'I' (uppercase) ↔ 'i' (lowercase)
• 'i' uppercased → 'I'
• 'I' lowercased → 'i'

But in Turkish:

• 'I' (dotless I) ↔ 'ı' (dotless i)
• 'İ' (dotted I) ↔ 'i' (dotted i)

Turkish has four distinct 'I' characters, not two!

What Goes Wrong:

Consider comparing "FILE" and "file" in a case-insensitive manner:

With English locale:

• "FILE".toLowerCase() → "file"
• "file" == "file" → true ✓

With Turkish locale:

• "FILE".toLowerCase() → "fıle" (dotless ı!)
• "fıle" == "file" → false ✗

This is a real bug that has affected:

• Microsoft Azure services
• Java applications run in Turkish locale
• Any software that uses system locale for case conversion

The Fix:

For case-insensitive comparison where locale shouldn't matter (identifiers, file names, protocol keywords), use invariant/neutral locale or ordinal comparison:

// Java: Avoid locale-specific case conversion
"FILE".equalsIgnoreCase("file")  // Uses default locale - dangerous!
"FILE".toLowerCase(Locale.ROOT).equals("file".toLowerCase(Locale.ROOT))  // Safe

// C#: Explicit ordinal comparison
string.Equals("FILE", "file", StringComparison.OrdinalIgnoreCase)

Let's examine how case sensitivity affects real-world scenarios:

1. User Authentication:

Username comparison: Usually case-insensitive for user convenience

• 'JohnDoe', 'johndoe', 'JOHNDOE' should all refer to the same account
• Store normalized (lowercase) version in database
• Display original casing for aesthetics

Password comparison: Always case-sensitive

• 'Password123' and 'password123' are different passwords
• Case contributes to password entropy
• Never normalize password case

2. Search Functionality:

User-facing search: Usually case-insensitive

• User searches for 'apple' and expects to find 'Apple', 'APPLE', 'apple'
• Normalize both query and indexed content to lowercase
• May also want accent-insensitive search ('cafe' matches 'café')

Technical search (code, logs): Often case-sensitive

• Searching for variable 'userName' shouldn't match 'USERNAME'
• Provide toggle for case sensitivity
• Regular expressions with /i flag for case-insensitive

3. URL and Web Handling:

Protocol and domain: Case-insensitive

• 'HTTP://EXAMPLE.COM' = 'http://example.com'
• RFC 3986 specifies this behavior

Path and query: Case-sensitive (usually)

• '/Users/Document.html' ≠ '/users/document.html'
• Depends on server's file system
• Query parameters often case-sensitive

4. File Extensions and Types:

• '.JPG', '.jpg', '.Jpg' should typically match as same type
• Check using case-insensitive comparison:

  if extension.lower() in ['.jpg', '.jpeg', '.png']:
  

5. Command-Line Arguments:

• Often case-sensitive: --verbose ≠ --VERBOSE
• Some tools support case-insensitive flags
• Document your tool's behavior clearly

Case sensitivity affects the correctness and efficiency of fundamental operations:

Hash Tables and Dictionaries:

Standard hash functions treat different byte sequences as different keys:

hash("Apple") ≠ hash("apple")

For case-insensitive dictionaries, you must:

• Normalize keys before hashing: hash(key.lower())
• Or use custom hash function: hash_ignorecase(key)

Consequences:

• Two keys that differ only in case will not collide (case-sensitive)
• They will collide (case-insensitive), which may be desired

Binary Search and Sorted Collections:

Case sensitivity affects ordering and thus binary search correctness:

# Case-sensitive sorted: ["Apple", "Banana", "apple", "banana"]
# Binary search for "apple" finds it at index 2

# Case-insensitive sorted: ["Apple", "apple", "Banana", "banana"]
# Binary search for "apple" might find "Apple" first

Important: You cannot use case-sensitive sort and then case-insensitive binary search! The ordering must match the comparison.

Tries and Prefix Trees:

Standard tries use characters as edge labels. Case sensitivity affects:

Case-sensitive trie:

         root
        /    \
       A      a
       |      |
       p      p
       |      |
       p      p
       |      |
       l      l
       |      |
       e      e

"Apple" and "apple" are separate paths

Case-insensitive trie:

         root
          |
          a (represents A and a)
          |
          p
          |
          p
          |
          l
          |
          e

"Apple" and "apple" share the same path

Implementation: Either normalize before insertion/lookup, or use a 26-element array instead of 52 for letters.

Suffix Arrays and Pattern Matching:

For case-insensitive pattern matching:

• Either normalize text and pattern before building suffix array
• Or use case-insensitive comparison functions
• KMP, Rabin-Karp, etc., all need case-aware comparison

For robust case-insensitive comparison, case folding is preferred over simple lowercasing:

What's the Difference?

Lowercasing: Converts uppercase letters to their lowercase equivalents using standard Unicode lowercase mappings.

"HELLO".toLowerCase() → "hello"
"STRASSE".toLowerCase() → "strasse"

Case Folding: A more aggressive normalization designed specifically for case-insensitive comparison. It handles special characters that lowercase alone misses.

"STRASSE".casefold() → "strasse"  // Same as lowercase
"ß".casefold() → "ss"            // Different! Lowercase keeps ß

Key Differences:

When to Use Which:

Use lowercasing when:

• You need to preserve round-trip capability (can uppercase later)
• You're normalizing for display, not comparison
• You're working with simple ASCII text
• You're storing a canonical form that users might see

Use case folding when:

• You're doing case-insensitive comparison
• You need to match user input regardless of case/accent
• You're building search indexes
• You don't need to reverse the transformation

Python Example:

# Lowercase: ß stays as ß
"straße".lower() == "strasse"  # False!

# Case fold: ß becomes ss
"straße".casefold() == "strasse"  # True!

Unicode Technical Standard:

The Unicode standard defines case folding in UAX #21. It's the recommended approach for case-insensitive matching when correctness matters.

We've explored case sensitivity in depth—from its binary origins to its impact on algorithms and international text handling. Let's consolidate the essential knowledge:

What's next:

Case sensitivity is one dimension of comparison complexity. The next page explores locale vs binary comparison—how different cultural conventions affect string ordering, why 'ä' might sort with 'a' or after 'z' depending on locale, and when to use each approach.