I was reading about extension methods in C# 3.0. The text I'm reading implies that an extension method with the same signature as a method in the class being extended would be second in order of execution - that is, the method in the sealed class gets called. If this is the case, how can you extend the sealed class ?
Indeed, the actual method takes precedence over the extension method. And just to make it clear - "order of execution" suggests both might be called; only the original method will be invoked. Perhaps pick another name / signature; you can't use extension methods to monkey-patch, if that is your intent.
If there is some base-class / interface (that the type implements) that doesn't have this method, you could perhaps cast it to there...?
Use another method signature. Extension methods imply that you are extending the sealed class with new functionality and not overriding the ones already implemented.
Extension methods have "hide-by-name" semantics with instance members on a type. This means that any accessible instance member on a type will always shadow any extension methods with the same name, even if the extension method is a better fit. As a result, if an instance member is ever added to a type with the same name as an extension method, then the extension method can be rendered uncallable.
For more details, take a look at this post: Extension Methods Best Practices (Extension Methods Part 6)
来源：https://stackoverflow.com/questions/2303885/if-an-extension-method-has-the-same-signature-as-a-method-in-the-sealed-class-w