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More in Extension Methods
What is an extension method, and what syntax makes a static method into one? How does method resolution priority work when an extension method has the SAME name and signature as an actual instance method on the type? How do you write a generic extension method that works with any collection type, like a custom 'IsEmpty()' check? How do you chain multiple extension methods together in a fluent style, and what design principle makes this possible? What are extension methods in C#, and how do they let you add functionality to a type you can't modify? How would you write an extension method on an interface (like IEnumerable<T>) that provides a default implementation shared across EVERY concrete implementing type? How would you write extension methods to build a lightweight, fluent validation/guard-clause library? Why can't extension methods be used to add STATIC members, operators, or FIELDS to an existing type, and what are the practical implications of this limitation? How do 'extension method ambiguity' conflicts arise when two different NuGet packages or namespaces define extension methods with the identical signature, and how do you resolve them? How would you write generic extension methods leveraging C# 11's generic math interfaces (like INumber<T>) to build a single reusable numeric utility working across int, double, decimal, and other numeric types?
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Why must extension methods be defined in a static class, and how does the compiler resolve a call to one?

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Answer

Extension methods are purely a COMPILE-TIME convenience — the compiler resolves 'obj.ExtensionMethod()' by rewriting it internally as 'StaticClass.ExtensionMethod(obj)', which requires the method to live in a static class; at runtime, there's no real difference from calling an ordinary static method.
public static class IntExtensions {
  public static bool IsEven(this int number) => number % 2 == 0;
}

int x = 4;
bool even = x.IsEven();          // syntactic sugar for:
bool even2 = IntExtensions.IsEven(x); // this equivalent static call
Real-world example Understanding that extension methods don't actually modify the extended type at all — they're purely compiler-level syntactic sugar.

Common follow-ups: Does this mean extension methods can access private members of the type they extend?

Fundamentals
All 11 Extension Methods questions