Download A First Course in Real Analysis, Second Edition by Murray H. Protter, Charles Bradfield Morrey PDF

By Murray H. Protter, Charles Bradfield Morrey

Many alterations were made during this moment variation of A First direction in genuine research. the main seen is the addition of many difficulties and the inclusion of solutions to lots of the odd-numbered routines. The book's clarity has additionally been stronger via the additional rationalization of a number of the proofs, extra explanatory comments, and clearer notation.

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Extra resources for A First Course in Real Analysis, Second Edition

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A number xis between a and b if both inequalities a< x and x < b are true. A compact way of writing these two inequalities is a< x

2(ii), which states that the negative of a sum is the sum of the negatives. 4. 2. Natural Numbers and Sequences 13 that -(-a)= a, we obtain the usual rule for the addition and subtraction of any finite number of terms. With the help of the sign laws for multiplication and the extended distributive law, we get the standard rules for the multiplication of signed sums. For example, it is easy to verify that (a 1 - a2 )(b 1 - b2 - b3 ) = a 1 (b 1 = a 1 b1 - b2 b3 ) - a2 (b 1 - a 1 b2 - a 1 b3 - - a2 b1 b2 - b3 ) + a2 b2 + a2 b3 • The symbol x", for n a natural number, is defined in the customary way as x · x · · · · · x with x appearing n times in the product.

We also use the double inequality 7

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