# Questions tagged [real-numbers]

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

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310 views

### Cardinal vs. ordinal: When learned? When needed?

Is the distinction between cardinal numbers and ordinal numbers taught as part of mathematics (as opposed to part of learning the language distinction between "one" and "first") in pre-college or ...
3k views

### Should high school teachers say “real numbers” before teaching complex numbers?

Before complex numbers are introduced in senior high school courses, should we emphasise that solutions (e.g. to quadratic equations) are real solutions? If we do, then when non-real numbers finally ...
7k views

### Why is it possible to teach real numbers before even rigorously defining them?

In mathematics, one can hardly study any mathematical concept unless it is clearly and rigorously defined. For example, without the definition the fundamental group, it is almost impossible to teach ...
878 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 ...
321 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 ...
488 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 ...
259 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 ...
142 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 ...
3k 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 ...
631 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 ...
692 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 ...
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 ...