Saturday, November 26, 2005

question of the day

"Mom, how do they know that infinity is the biggest number?"

She's only just turned 7.

A lively discussion ensued, involving the almost-9 and almost-5-year-olds as well.

UPDATE: Tom gives a mini-lecture in the comments. Here's a paraphrase of my answer (since I can't remember my exact words): "Infinity is not a number, it's an idea." That was the basis of the lively discussion.

1 comment:

Sheik Yerbootie said...

Ahem - allow an expert to explain.

Infinity is not a number; it is the name for a concept.

There are no numbers bigger than infinity, but that does not mean that infinity is the biggest number, because it's not a number at all. Infinity is neither even nor odd.

You can think of the set of natural numbers (numbers like 1,2,3,4,5,...) as countably infinite - meaning that you can never stop counting.

The other type of infinity is uncountable, which means there are so many you can't 'number' them.

Can one have infinity plus one?

Yes. That would be infinity - plus one.

And there you have it - brilliant!!!

Now, let's discuss infinity as a concept in geometry.

On second thought, let's not.