Questions tagged [real-numbers]
For questions on teaching and introducing real numbers and properties of real numbers.
20 questions
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Why are negative numbers introduced before quotients in the real number subsets?
This is a question regarding why the order of the real number subsets commonly used in the mathematics community is such:
$$ \mathbb{N}\subseteq\mathbb{Z}\subseteq\mathbb{Q}\subseteq\mathbb{R} $$
Here ...
- 29
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What is the best didactical way to read decimal numbers?
What is the best didactic and number sense-promoting method for reading decimal numbers?
For instance, is it best to teach students to read the number 3.14 as 'three and fourteen hundredths' instead ...
- 2,408
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Should an undergraduate math program contain a course on Lebesgue integration?
Is it standard for a math undergraduate program to have a course on Lebesgue integration?
Does Riemann integral suffice for undergraduates?
The reason of my question is I read a paper by Bartle titled ...
- 203
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3
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How many zeros do we need to add to get a nonzero value?
A student (kid) of mine asked this question to me. I am not sure what to make of it or how do I answer it.
How many zeros do I need to add to get a non-zero value?
...
- 391
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Why is highschool math so unrigorous?
I am an highschool student (I'm starting soon the italian equivalent of 12th grade) and I have many problems with the way hs math education works. I don't understand why everything is explained only ...
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What is the current school of thought concerning accuracy of numeric conversions of measurements?
I posted this question earlier today on the Mathematics site (https://math.stackexchange.com/q/3988907/96384), but was advised it would be better here.
I had a heated argument with someone online who ...
- 925
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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 ...
- 30.2k
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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 ...
- 510
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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 ...
- 4,295
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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 ...
- 10.9k
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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 ...
- 1,673
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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 ...
- 874
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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 ...
- 287
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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 ...
- 5,030
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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 ...
user5799
14
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2
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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 ...
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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 ...
user230
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11
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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 ...
- 1,528
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7
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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 ...
- 2,008
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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 "...
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