# Tag Info

Accepted

• 12.3k

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

Here is a simpler definition of limits which works better for monotone sequences, and has value in motivating further investigation of the concept of limits: If a sequence $x_1, x_2, ...$ is ...
• 529

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

While monotone behavior is important in analysis (such as the monotone convergence theorem in measure theory), I think you should forget the emphasis on monotone behavior and just be honest with the ...
• 3,536

### 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 ...
• 26.4k

### 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 ...
• 1,828

### 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 ...
• 1,078
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

### 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 ...
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 ...
• 11
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 ...
• 4,438

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