Chapter 2: Numeration Systems and Sets

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Chapter 2: Numeration Systems and Sets

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Chapter 2: Numeration Systems and Sets
1 Section 1: Numeration Systems

The number system we use now is a base 10 system, and the written symbols we use are called numerals. throughout history, other numerals and base systems have been used. Here is a table depicting some of those systems in relation to our own: A Numerations system is a set of symbols and rules that define numbers systematically. Our system, the hindu-arabic system, defines our way of looking at numbers, and we use 10 symbols: 0,1,2,3,4,5,6,7,8, and 9. Different Base Systems: in a base 5 system, 5 is zero, or 10. let's look: 1,2,3,4,5 are the only numbers we use, and we do not write 5, we write "10" so here is a table: Base 10 Base 5 1 1 2 2 3 3 4 4 5 10 6 11 7 12 8 13 9 14 10 20 11 21 12 22 Since it is base 5, 5 is never written and instead it is written an 10, 20,...so on and so forth. The more we understand different number systems, the more insight we gain into our own. In this section I learned all about lace values: 546 is 5 x 100 + 4 x 10 + 6 x 1 and how to convert from one system to another by using place values as a guide. for example: to convert 25 to base 2:

2 Section 2: Describing Sets

In this section, we did a lot of algebra review of sets, which are a way to organize a collection of data into an easily understood collection. the elements of the set are the individual pieces of info in the set. Here is an example of a set: D={} the numbers are the "elements" or "members" of the set. this method of writing a set is called the Listing method. Another way to write a set is called "Set Builder Notation" You read this as: C= { x | x ∈ W} C is equal to the set C= { of all elements x x such that | x is a whole number x ∈ W} We learned about how if 2 sets have the same elements then they are equal. We also defined a subset as a set containing some but not all the elements of another set. This section was very fun and helped a lot in the next chapters.

3 Section 3: Other Set Operations and Their Properties

In this section, we talked about the intersection of sets. I learned that to describe the intersection of 2 sets, we use a U symbol. the intersection of sets A and B is written as: A∪B. The intersection of both sets is written as A∩B. We looked closely at how one set interacts with another and how to determine the intersection of 2 or more sets.

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