Proud!

[la_rainette]

Yesterday, my Froglet tackled the concept of infinity.

Froglet: Is there a Highest Number?
rainette: ?
Froglet: Yes, is there a number after which there are no more numbers? A Last Number?

I had a moment of unbelievable pride at this. My Froglet comes up with the greatest questions, really. So I beamed, congratulated her warmly (to which she answered with the braying, unelegant laughter of embarrassed pride), and tried to explain the Concept of Infinity, and why her question was so incredibly sharp.

Which is when I realized that maybe it wasn't.

Froglet: But. But. Mommy?
rainette: yes, my Froglet?
Froglet: What comes after one hundred?
rainette: !

It was still incredibly sharp and I am very proud of her, even if infinity to her starts at one hundred.

Comments

[seshat1.livejournal.com]

Wow! A future mathematician =D

[la-rainette.livejournal.com]

:D If she ever gets past her "one hundred" block, infinity's the limit ;)

[darthfox.livejournal.com]

[plotzes]

[la-rainette.livejournal.com]

:D Isn't she just brilliant?

[raesa.livejournal.com]

It was still incredibly sharp and I am very proud of her, even if infinity to her starts at one hundred.

That story has to be one of the most adorable things I've ever heard in my entire life! And yes, she is incredibly sharp to have even come up with a question like that at her age. As for infinity starting at one hundred... Well, we all have to start somewhere, right? Why shouldn't she start there. She's already way ahead of the game, so her infinity will grow in no time.

However, in the meantime, infinity definitely begins at one hundred, and Froglet is definitely the most adorable thing ever.

[la-rainette.livejournal.com]

Thank you *hugs* I think so too *proud mom smile*

[l33tminion]

Little kids ask the best questions.

This reminds me of a math problem from way back when (5th grade, actually, I think):

"The Hotel Infinity has an infinite number of rooms. The rooms are numbered 1, 2, 3, 4, and so on. One night, the Infinity Conference was going on at the hotel, so the hotel had an infinite number of guests (occupying rooms 1, 2, 3, 4, and so on). Suddenly, an infinite tourist bus pulled up to the hotel, also with an infinite number of guests. The desk clerk was worried for a minute, but then thought of a way for all the guests to stay at the hotel (without putting multiple people in the same room). What was the clerk's solution?"

[la-rainette.livejournal.com]

Uh, I confess I don't get it. Infinity being infinite by definition, is there really a problem? I mean, infinite+infinite is infinite, and your hotel has an infinite number of rooms.

(But if there is another solution, I am DYING to know!)

[l33tminion]

You're quite correct, but that's in the problem. It's not the solution (in fact, it is the fact that the solution proves). The solution needs to be more specific. The question is how, exactly, did the clerk accomplish this, not is it possible (which it is).

For example, the clerk can't just move each old guest down an infinite number of rooms (to rooms infinity, infinity + 1, infinity + 2, etc.) because there are no numbers beyond infinity.

[l33tminion]

All right, here's the solution. The clerk moved the person from each room to the room with twice that number (from 1, 2, 3, etc. to 2, 4, 6, etc.). That leaves an infinite number of rooms open (rooms 1, 3, 5, etc.) and requires each guest to walk only a finite distance.

An interesting thing to know is that the number of even positive integers is the same as the total number of positive integers, even though only half of the positive integers are even (this applies to odd integers as well).

How can this be shown? A good place to start is to ask how you know the following sets have the same number of items without using a clearly defined number: {a,b,c} and {x,y,z}

The way you know that these sets have the same number of items is that there is a one to one correspondence (a corresponds to x, b to y, and c to z). Our infinite sets are: {positive integers} and {even numbers}

These also have a one to one correspondence, as each positive integer n corresponds to exactly one even number 2n. Therefore, the sets are the same size. (To be specific, these sizes are countable infinity. There are also larger, uncountable infinities, such as the number of real numbers.)