# Tag Info

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### In what grade do kids (New York, US) learn common differences?

This is a topic I could imagine not being adequately covered in all U.S. schools, although (as Dave L. Renfro pointed out in a comment), it is listed in the Common Core Mathematics standards under ...

### What is the intuition behind the limit superior?

Every sequence $\langle u_n: n\in\mathbb{N}\rangle$ has a natural extension $\langle u_n: n\in{}^\ast\mathbb{N}\rangle$ where ${}^\ast\mathbb{N}$ are the hypernatural numbers (positive hyperintegers). ...

### How can I introduce a speech about the Fibonacci sequence creativiely?

ADVICE: When you have a question about a speech, you should give us more information to help you. Especially how long is the speech (it affects how much intro you do). But also the audience. And ...

### Teaching limits of sequences before limits of functions in Calculus?

When you look at the formal definitions of several concepts in real analysis you see that those concepts are rooted in the limit of sequences (or better to say, these concepts can be defined in a way ...

### What is the intuition behind the limit superior?

I would probably avoid the phrase "at infinity", since it's kind of vague and I'm not sure if it'd help someone who doesn't already understand the concept. Instead, I would talk more explicitly about ...

### Motivation for Fibonacci: Bees

After looking at Tony Jacobs argument, here is an argument of my own. Start with a single male. At each generation, let $m_n$ and $f_n$ be the total number of males and females respectively, and let ...
Accepted

### Motivation for Fibonacci: Bees

You can see it by breaking the numbers $s_n$ into parts: $s_n=f_n+m_n$, which represent the number of female and male bees, respectively, at each level of the family tree. To find $f_{n+1}$, we note ...

### What is the intuition behind the limit superior?

For me, this picture from wikipedia helped the most in understanding limsup and liminf
1 vote

### Is this motivation for the concept of a limit a good one?

Two points to think about: It might be more intuitive to replace "from some $N$ onward" by "for all $n$ except finitely many". I often present the notion of a limit through a game:...
1 vote

### What is the intuition behind the limit superior?

Limit supremum (of a sequence of numbers) I will try to give intuition only using words, without using mathematical symbols. What is the smallest number which is greater than infinitely many members ...
1 vote

### Any metaphors/intuitions for a limit of a sequence?

Here is my "unfinished" attempt that I used in one of my classes last year. Generally speaking, it is based on the idea of "proof-generated definitions" introduced by Lakatos. As such, the question is ...
1 vote

### How can I teach my students the difference between a sequence and a series?

First answer: Isn't sequence like a list of numbers that appear as according to function? And series is more like the addition of the terms of the sequence. I guess There convergence properties differ ...

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