# Tag Info

### The concept of infinity for a 5 year old

This does not directly concern the $\infty+1=\infty$ issue and I am not certain that I understand what you mean by his previous understanding of mathematics, but I wanted to give the following ...
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### The concept of infinity for a 5 year old

First of all, regardless of age, people need to understand that "infinity" is not a number, and not a placeholder for a number, but an attribute of them (i.e. the fact that you can increase numbers ...
• 848
Accepted

### The concept of infinity for a 5 year old

On a piece of paper, he started with writing 10, then 100, then 1000, .... and he stopped after writing 40 zeros with 1. Then he came to me and said, "I understand infinity now; infinity is a number ...
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### The concept of infinity for a 5 year old

I'm not sure why the two basic things adults seem to say about infinity are "infinity is not a number" and "∞+1=∞", both of which are at best misleading. (Infinity doesn't name a number, but it does ...
• 11.6k

### The concept of infinity for a 5 year old

Speaking as someone who was that kid, you might be able to explain $\infty + 1 = \infty$ via the Hilbert hotel. Imagine a hotel that has an infinite number of rooms, one for every number. Imagine the ...
• 261

### Nice examples of limits to infinity in real life

If you are willing to take some time to explain the model and do some simulation, I really like to show students a logistic growth model (in discrete time). The basic setup is something like the ...
• 8,225
Accepted

### The concept of infinity for a 5 year old

I would start by saying something along the following lines... "You're asking some very grown-up questions for someone that's only 5. Are you ready to do some really, really, grown-up thinking about ...
• 1,224
Accepted

### 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 ...
• 11.6k

### Can we explain to undergraduates how points make a line?

I agree with the premise, lines are (in some way) made out of points, and points have no length. If, restricting ourselves to a straight line, we can consider these as subsets of the real numbers ...
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### Would teaching nonstandard calculus in an introduction calculus course make it easier to learn?

It's not really that relevant since the bulk of a normal calculus course (e.g. AP BC, Thomas Finney, Stewart) just does a small amount of epsilon-delta (so student is exposed to it) and then moves to "...
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### Motivating example for sequences, sums and limits in high school

The common puzzle of giving a few terms and asking for the next are examples of (generating) sequences by some particular rule. A series is just a sequence, summed together. Ask e.g. for the sum \$1 + ...
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