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MTE1501 ASSIGNMENT 03 DUE 18 JULY 2023
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,MTE1501 ASS 033.1 LU1: MATHEMATICS IN SOCIETY
Read section 1.3: Defining Mathematics - in your study guide and provide the
differences between the three views used to outline the mathematics consideration.
(Page 2 + 3 + 4
According to section 1.3 of the study guide, the three views used to outline the
consideration of mathematics are as follows:
1. The Platonist View: This view sees mathematics as a discovery of an unchanging and
eternal realm of ideas. It suggests that mathematical objects and concepts are abstract
entities that exist independently of the human mind. Platonists believe that
mathematicians uncover these mathematical truths through their reasoning and
exploration.
2. The Formalist View: In contrast to the Platonist perspective, formalists see mathematics
as a human construct based on logical rules and symbols. They argue that mathematical
objects are not inherently real or existing independently, but rather are defined within a
formal system created by humans. Formalists view mathematics as a game with its own
set of rules and symbols, where deductions and computations can be made based on
these rules.
3. The Instrumentalist View: The instrumentalist view considers mathematics as a useful
tool rather than a discovery or a human construct. Instrumentalists focus on the utility and
applicability of mathematics in solving real-world problems. They argue that mathematical
concepts are simply tools created by humans to model and describe different aspects of
the world, and their validity lies in their ability to provide accurate predictions and
explanations.
, Overall, these three views provide different perspectives on the nature of mathematics,
whether it is a realm of abstract entities, a system of logical rules, or a practical tool.
3.2 LU2: TEACHING AND LEARNING MATHEMATICS
3.2.1. Do the following:
1. Explain why the word “natural numbers” is used when referring to counting numbers.
The word "natural numbers" is used when referring to counting numbers because these
numbers represent the most basic and fundamental way of counting or enumerating
objects. Counting is a natural human activity that has been practiced since ancient times to
keep track of quantities or measure the size of collections.
The term "natural" in this context refers to the innate or inherent nature of these
numbers. They arise naturally when we start counting objects or things in the world
around us. For example, if we have one apple and we add another apple, we naturally
come up with the concept of "two" to describe the combined quantity. Similarly, if we
have two apples and add another one, we naturally arrive at the concept of "three".
In essence, the term "natural numbers" emphasizes the intuitive and instinctive nature of
counting, as opposed to more abstract or complex mathematical concepts. It reflects the
simple and fundamental process of counting that humans have been doing for thousands
of years, making it an appropriate term to use when referring to these numbers.
2. Which of the following statements are True or False? Where it is FALSE, provide
explanation for your answer.
(a) No integer is an irrational number. (Page 59, 60, 61)
(b) Every integer is a rational number. (Page 59, 60)
(c) Every integer is a whole number. (Page 59, 60ng it an appropriate term to use when
referring to these numbers.
(a) False. An irrational number is a number that cannot be expressed as a fraction or a
ratio of two integers. While integers can be expressed as fractions with a denominator of
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