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Notice how adding please allows you to achieve a friendly, polite tone without diminishing the strong, directive attitude that comes from using the imperative You might phrase the announcement of the new microbiology lab as Send us your microbiology tests and discover the difference in quality and speed our new facility makes Or you could say, Please send us your microbiology tests and discover the difference in quality and speed our new facility makes Which do you prefer Some people feel that the tone is less professional when you add the word please in this circumstance, almost as if you re begging Others think it s courteous and more formal Neither is right, just as neither is wrong in this example; the sentences have a different feel from one another, that s all Part of your decision will be based on your comfort level Not everyone is comfortable using the authoritative tone of the imperative And some people perceive that using please adds a tone of pleading that sounds unprofessional in standard business writing Use your best judgment on a case-by-case basis Sometimes you imply a reference to the reader by constructing your sentence to create a sense of connection between you, the writer, and your readers For example, in the sentence It s important to check your credit on an annual basis, you re implying a reference to the reader Depending on the target audience, this sentence is really saying It s important (if you own a home) to check your credit on an annual basis, or It s important (if you intend to buy a home) to check your credit on an annual basis, or It s important (for you) to check your credit on an annual basis

public interface ISeries<T> where T : class {

When this version of ISeries is implemented, the implementing class must also specify the same constraint for T, as shown here:

class ByTwos<T> : ISeries<T> where T : class {

Notice that each x in the domain has just one y value corresponding to it Thus, even though we cannot give a formula for the function, the curve is the graph of a function The domain of this function is ( , 3) ( 5, 7)

Because of the reference constraint, this version of ISeries cannot be used on value types Thus, in the preceding program, only ByTwos<ThreeD> would be valid ByTwos<int> and ByTwos<double> would be invalid

Sometimes you will want to compare two instances of a type parameter For example, you might want to write a generic method called IsIn( ) that returns true if some value is contained within an array To accomplish this, you might first try something like this:

// This won t work! public static bool IsIn<T>(T what, T[] obs) { foreach(T v in obs) if(v == what) // Error!

the domain has corresponding to it precisely one y value is this: If every vertical line drawn through a curve intersects that curve just once, then the curve is the graph of a function

18:

return true; return false;

Implying a reference to your readers is a subtle and effective technique, and it serves to increase your Empathy Index

Unfortunately, this attempt won t work Because T is a generic type, the compiler has no way to know precisely how two objects should be compared for equality Should a bitwise comparison be done Should only certain fields be compared Should reference equality be used The compiler has no way to answer these questions Fortunately, there is a solution To enable two objects of a generic type parameter to be compared, they must implement the IComparable or IComparable<T>, and/or IEquatable<T> interfaces Both versions of IComparable define the CompareTo( ) method and IEquatable<T> defines the Equals( ) method The IComparable interfaces are intended for use when you need to determine the relative order of two objects IEquatable is used for determining the equality of two objects These interfaces are defined by the System namespace, and they are implemented by all of C# s built-in types, including int, string, and double They are also easy to implement for classes that you create Let s begin with IEquatable<T> The IEquatable<T> interface is declared like this: public interface IEquatable<T> The type of data being compared is passed as a type argument to T It defines the Equals( ) method, which is shown here: bool Equals(T other) It compares the invoking object to other It returns true if the two objects are equal and false otherwise When implementing IEquatable<T>, you will usually also need to override GetHashCode( ) and Equals(Object) defined by Object, so they act in a manner compatible with your implementation of Equals( ) The program that follows shows an example Using IEquatable<T>, here is a corrected version of IsIn( ):

// Require IEquatable<T> interface public static bool IsIn<T>(T what, T[] obs) where T : IEquatable<T> { foreach(T v in obs) if(vEquals(what)) // Uses Equals() return true; return false; }

Until we learn some more sophisticated techniques, the basic method that we shall use for graphing functions is to plot points and then to connect them in a plausible manner