Questions tagged [real-numbers]

For questions on teaching and introducing real numbers and properties of real numbers.

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0answers
61 views

“Small” real numbers [duplicate]

At least for me, my intuition for what numbers are large or small comes entirely from positive numbers. I find it challenging to use the word "small" correctly when talking about negative numbers. ...
18
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5answers
733 views

Inability to work with an arbitrary mathematical object

This question is motivated by student responses to homework and quiz problems I have recently posed in an undergraduate real analysis course. I will share some examples and observations first, to ...
6
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2answers
299 views

How to teach real analysis?

I am recently going to make a series of videos about real analysis and measure theory. I wonder if anyone can give me some suggestions on how to arrange the material of the course. Should I introduce ...
7
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4answers
478 views

What number is the sum of two roots

This is one of these questions that students ask and for which I have never found an answer that students would accept as convincing. Here is an instance: Student: 2•3 is a number, namely 6. 2+3 is a ...
8
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1answer
248 views

Why many people believe that: $\displaystyle c>0\implies \frac{1}{c}<0$?

I came across many people who believe the below false implication. I don't know why people believe it true in high school and middle school and also students in university level. Really I would like ...
6
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3answers
141 views

Specific Intervention(s) for Middle School 'Place Value' confusion

I'm working with a middle school student (grade 8) who recently displayed a misunderstanding of place value in decimal numbers. The student believes, for example, that $0.125$ is bigger than $0.12$ in ...
8
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3answers
2k views

How to practically teach surds?

In teaching Middle School students (often around year 8 or 9), the topic of surds comes up here (I have to teach this topic) - and is often met with derision on commencement of the topic and during ...
14
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2answers
507 views

How the real numbers are taught?

I'm interested to know how the real numbers are introduced at beginner level in different countries. In my (old) experience of teacher in Italy there was some well defined steps: 1) Introduce the ...
17
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6answers
649 views

What is a number?

In a set theoretic point of view all mathematical objects are sets. We "call" some of them as numbers (e.g. sets in $\mathbb{N}$, $\mathbb{Q}$, $\mathbb{R}$, $\mathbb{C}$, $Ord$, $Card$) but what is ...
22
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10answers
2k views

Redundant zeros

How to convince a middle school student that $0.50=0.5=0.500=\cdots$? I used the fact that $0.50=\frac{5}{10}+\frac{0}{100}=\frac{5}{10}=0.5$ but that far from intuitive. Then I tried to explain ...
12
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7answers
355 views

What different ways do people use to show students that $\mathbb{R}$ is uncountable?

In particular, if you use Cantor's diagonalization argument, do you ignore the repeating decimal annoyance? Or prove that it's not a problem? Is there another clean way that gives students intuition ...
25
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6answers
1k views

Good definition for introducing real numbers?

In the first lectures about calculus/analysis, you should introduce real numbers. Let's assume students know that rational numbers are. What are the advantages or disadvantages in the different "...