Questions tagged [infinity]

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21 votes
13 answers

How can I familiarize elementary school students with infinities larger than $\aleph_0$?

Cantor's discovery of the existence of more than one infinity was a revolutionary change in human knowledge. He defined the notion of counting by bijections and showed that one can use infinities as ...
1 vote
4 answers

Reasoning outcomes of simplifications involving infinity

There are some cases where final result looks like strange when the concept of infinity involves. My issue is how to describe these situations to our students. Here are few examples ; When you keep ...
7 votes
8 answers

Nice examples of limits to infinity in real life

I have to teach limits to infinity of real functions of one variable. I would like to start my course with a beautiful example, not simply a basic function like $1/x$. For instance, I thought of using ...
7 votes
6 answers

Motivating example for sequences, sums and limits in high school

I currently work as a substitute teacher at a local high school and the topic in one of the classes is sequences, series and limits. Because I always disliked learning about a topic without having ...
1 vote
1 answer

Intuition explanation about Lebesgue measure zero of the rational numbers [closed]

This is a question about the intuition of the rational number having measure zero. Let us consider followng proof: Let $I = [0,1]$ and $Q = \mathbb Q \cap I$ and let $\lambda$ be the Lebesgue measure. ...
6 votes
3 answers

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 ...
48 votes
21 answers

The concept of infinity for a 5 year old

My son, who just turned 5, has been interested in the concept of infinity since long. He asks me a lot of questions regarding infinity. For example, not accepting my infinity + any number = infinity, ...
5 votes
4 answers

Would teaching nonstandard calculus in an introduction calculus course make it easier to learn?

Nonstandard calculus is a reformulation of calculus that is based on infinitesimals instead of epsilon-delta definitions. Of course, people had tried to use infinitesimals in calculus before; in fact, ...
2 votes
0 answers

Are there any books on how mathematicians reason about infinite sets? [closed]

From: Philip Johnson-Laird BA PhD Psychology (UCL), Stuart Professor of Psychology Emeritus at Princeton. (Author isn't a logician.) How We Reason (1st edn 2008). p. 457. For an account ...
13 votes
6 answers

Can we explain to undergraduates how points make a line?

Many of my students arrive in college believing that lines are (in some way) made out of points. They also believe that points have no length. They want to know how a bunch of zero length points ...
10 votes
1 answer

Looking for a specific female maths writer, who has written on infinity

I once read a book on infinity that was written by an American female maths writer. Her writing was very easy to read and she was a great explainer of concepts. A very distinct aspect of her books was ...