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BaronB@yahoo.com is my email, and I like listening to my students
As your first assingment, I need you to watch this video from khan
It is ofen said that mathematics is the language of science. If this is true, then the language of mathematics is numbers. Te earliest use of numbers occurred 100 centuries ago in the Middle East to count, or enumerate items. Farmers, cattlemen, and tradesmen used tokens, stones, or markers to signify a single quantity—a sheaf of grain, a head of livestock, or a fxed length of cloth, for example. Doing so made commerce possible, leading to improved communications and the spread of civilization. Tree to four thousand years ago, Egyptians introduced fractions.
Topic 1
assignment: 1
assignment due: jan/ 19 /2022 at 16:30 pm
Tey frst used them to show reciprocals. Later, they used them to represent the amount when a quantity was divided into equal parts. But what if there were no cattle to trade or an entire crop of grain was lost in a food? How could someone indicate the existence of nothing? From earliest times, people had thought of a “base state” while counting and used various symbols to represent this null condition. However, it was not until about the ffh century A.D. in India that zero was added to the number system and used as a numeral in calculations. Clearly, there was also a need for numbers to represent loss or debt. In India, in the seventh century A.D., negative numbers were used as solutions to mathematical equations and commercial debts.
Topic 2
assignment: 2
assignment due: Feb/ 2 2/2022 at 3: 00 pm
Te opposites of the counting numbers expanded the number system even further. Because of the evolution of the number system, we can now perform complex calculations using these and other categories of real numbers. In this section, we will explore sets of numbers, calculations with diferent kinds of numbers, and the use of numbers in expressions. Classifying a Real Number Te numbers we use for counting, or enumerating items, are the natural numbers: 1, 2, 3, 4, 5, and so on. We describe them in set notation as {1, 2, 3, . . .} where the ellipsis (. . .) indicates that the numbers continue to infnity.
Topic 3
assignment: 3
assignment due: Jan/ 27/2022 at 6:00 pm
Te natural numbers are, of course, also called the counting numbers. Any time we enumerate the members of a team, count the coins in a collection, or tally the trees in a grove, we are using the set of natural numbers. Te set of whole numbers is the set of natural numbers plus zero: {0, 1, 2, 3, . . .}. Te set of integers adds the opposites of the natural numbers to the set of whole numbers: {. . ., −3, −2, −1, 0, 1, 2, 3, . . .}. It is useful to note that the set of integers is made up of three distinct subsets: negative integers, zero, and positive integers. In this sense, the positive integers are just the natural numbers. Another way to think about it is that the natural numbers are a subset of the integers. negative integers zero positive integers . . . , −3, −2, −1, 0, 1, 2, 3, . . . Te set of rational numbers is written as { _ m n ∣m and n are integers and n ≠ 0 }.
Topic 4
assignment: 4
assignment due: Jan/ 31 /2022 at 10:00 pm
Notice from the defnition that rational numbers are fractions (or quotients) containing integers in both the numerator and the denominator, and the denominator is never 0. We can also see that every natural number, whole number, and integer is a rational number with a denominator of 1. Because they are fractions, any rational number can also be expressed in decimal form. Any rational number can be represented as either: 1. a terminating decimal: 15 ___ 8 = 1.875, or 2. a repeating decimal: 4 ___ 11 = 0.36363636 … = 0. _ 36 We use a line drawn over the repeating block of numbers instead of writing the group multiple times.
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