Banach Spaces of Continuous Functions by Zbigniew Semadini

By Zbigniew Semadini

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4 33 Using Junes to represent situations One of the things that funes are used for is to represent situations. Look at Activity 2(c), for example. The first sentence says that Z12 and H must be defined. These are statements that come before the definition of the fune begins. Now you are ready to define the fune. You have to decide if you are going to assign it to a variable and what name to use. The second sentence of the activity tells you that there is to be a single input parameter and it is suggested that its name be x.

11. The same as the previous activity for the relation (ab)2 = a2b2. 2 Definition of a group In the activities at the beginning of this section you constructed many mathematical systems and examined their properties. More specifically, you constructed certain sets, defined operations on them and studied various properties of these sets under the operations. For example, you constructed the set 8 3 of all permutations of {I, 2, 3} , defined the "product" of any two such permutations and checked that this operation satisfies the properties of closure, associativity, existence of an identity element, and the existence of an inverse permutation for every permutation.

Before doing that, however, make sure you write down a careful description of what these transformations are doing. Using both types of transformations several times over, we can calculate the negation of more complicated expressions. ) See if you can play the game with Activity 7(e). You might also derive some fun from recalling (or finding in a Calculus book) the definition of when a function f is continuous at a point a, and formulating what it means for f not to be continuous at a. 8 1. Mathematical Constructions in ISETL Miscellaneous ISETL features There are a number of ISETL features that are not extremely important for this course, but we wiJI mention them briefly because they might be encountered occasionally.

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