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Try Response.TransmitFile() to explicitly send the file from your ASP . NET application. This will cause a Open / Save As dialog box to pop up ... Adding these two equations gives (a + c) + (b + d) = (a + c) + (b + d) hence (a + c, b + d) is related to (a + c, b + d) Thus adding two of our equivalence classes gives another equivalence class, as it should We say that addition of integers is well de ned This point is so signi cant that it bears repeating Each integer is an equivalence class that is, a set If we are going to add two integers m and n by choosing an element from the set m and another element from the set n, then the operation that we de ne had better be independent of the choice of elements This is another way of saying that we want the sum of two equivalence classes to be another equivalence class We call this the concept of well de nedness EXAMPLE 51 To add 5 and 3 we rst note that 5 is the equivalence class [(2, 7)] and 3 is the equivalence class [(2, 5)] We add them componentwise and nd that the sum is [(2 + 2, 7 + 5)] = [(4, 12)] Which equivalence class is this answer Looking back at our prescription for giving names to the equivalence classes, we see that this is the equivalence class that we called 12 4 or 8 So we have rediscovered the fact that 5 + 3 = 8 Now let us add 4 and 9 The rst of these is the equivalence class [(3, 7)] and the second is the equivalence class [(13, 4]) The sum is therefore [(16, 11)], and this is the equivalence class that we call (16 11) or 5 That is the answer that we would expect when we add 4 to 9 Next, we add 12 and 5 Previous experience causes us to expect the answer to be 17 Now 12 is the equivalence class [(19, 7)] and 5 is the equivalence class [(7, 2)] The sum is [(26, 9)], which is the equivalence class that we call 17 Finally, we can see in practice that our method of addition is unambiguous Let us redo the second example using [(6, 10)] as the equivalence class denoted by 4 and [(15, 6)] as the equivalence class denoted by 9 Then the sum is [(21, 16)], and this is still the equivalence class 5, as it should be Remark 54 What is the point of this section Everyone knows about negative numbers, so why go through this abstract construction The reason is that until one sees this construction, negative numbers are just imaginary objects placeholders if you will which are a useful notation but which do not exist Now they do exist They are a collection of equivalence classes of pairs of natural numbers This collection is equipped with certain arithmetic operations, such as addition, subtraction, and multiplication We now discuss these last two If A = [(a, b)] and C = [(c, d)] are integers, then we de ne their difference to be the equivalence class [(a + d, b + c)]; we denote this difference by A C. itextsharp remove text from pdf c#: PDF : Remove content from PDF page. Redaction marks. - VintaSoft c# pdf viewer component Displaying the contents of a PDF file in an ASP . NET application ...
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