Gifted Issues Discussion homepage Forums General Discussion soliciting your opinion.......

I need help in answering a math question. I figured this would be a great place to get a good answer.

DD6 asked tonight: "what is infinity plus infinity?"

I said: infinity

DH said: 2(infinity)

Who is right? And for you more diplomatic people what is correct if neither are right?

If consensus is DH is correct, I will concede(grudgingly)

I don't think you can have 2 infinity. Infinity is just infinity. (IMHO!) I think of it kind of like 0 X 12(or any other number). It isn't 12 0's, it is just 0.

It did make me think of Toy Story though. "T(w)o infinity and beyond!!!"

DS7 had the same question last year. I googled the answer: infinity. And the answer to what is infinity minus infinity is: there is no answer, although some say infinity.

My opinion? Should have laughed when DH said '2(infinity)', maybe added 'and beyond!'

I think the correct answer would be similar to dividing by zero, you can't do it.

ETA: EandCMom sneaked the joke in on me!

I knew I could count on you guys.......awww........shucks!

Love the toy story reference::::: ROFL

Dottie, I don't understand what you just said except for that you said that DH is wrong!

Love that, too, OHG EandCMom!!! HI-larious!

There is such a thing as negative-infinity though. That might interest DD...

Details, Kriston, you can't think I'll be able to explain this stuff on my own now............................................

Dottie I think I maybe understand the 3 thing (simplistically of course!). Kind of like 3infinity/infinity where the infinities cancel each other out and leave 3?

Kriston - am I going to have to pull a 'neato foot stomping fit???? Giving OHG my credit - sheesh!!! ROFL!!!!!!!!

(just kidding OHG!!!! )

Show off!

;p

This is such a fun party! Kind of reminds me of the fun we had when we were discussing that club we were all going to join. Come to think of it, I don't think I've received checks from all of you, to cover dues yet.........

Uh oh. I see the administrator on line....

Shhhh keep it down ladies........ we need to keep the hi-jinks and shenanigans on the down low.....

LOL!!!! What do you mean you never received my check? Ummmmm.....the check is in the mail.....yeah, that's it!!!! ROFL!!!!

As for showing off, Dottie hasn't gently corrected me yet, but I'm expecting it any minute!!!!

Oh...thank you.........I so needed a few minutes of hearty laughter!

p.s.- if you check your bank records you'll see that the check has already been cashed.

Bummm...Bummmm....Bummmmmmmmmmmmmmmmmmmmmmmmmmmmmm

There is a math field cold Set Theory which covers problems exactly like this. From their point of view infinity + infinity is infinity and has the same size.

They use aleph-null as the cardinality of natural numbers = the size of all natural numbers, kind of infinity. As long as you can map set of numbers to natural numbers it still has a size of aleph-null. Doubling set of size aleph-null will give you only a set of size aleph-null since the numbers can still be mapped to the set of natural numbers.

There is such a thing as countably infinite sets (the size of natural numbers) and uncountable sets.

If you look at all real numbers, you will find out that there are many more real numbers and they can no longer be mapped to the natural set. The size of it is 2 to the power of aleph-null. Here you go, that's a completely different "infinity" that all natural numbers.

Tell DD that doubling won't change anything, but 2^ will do the trick

I hope I didn't mess it up too much. It has been a while since I took Theory of Sets.

Thanks LMOM! Over my head but I'm pretty adept at shortening my learning curve when I apply myself.

"Don't MAKE me break out L'Hopital's rule...."

Dare I ask?

Bummmmmmmm.....Bummmmmmmmmm....Bummmmmmmmmmmmmmmmmmmmmmmmmm

I just googled it!!!
You're just mean... ;p

Can the lion and bear still be friends................

LOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOL!

The music.............PERFECT!

Your sense of humor is just too perfect....please be my friend!

I do not get the lion and bear reference, but I love the clip anyway. Perfect "Bum Bum BUMMMMM" music there!

Here's the Wikipedia entry for negative infinity: http://en.wikipedia.org/wiki/Negative_infinity

Basically, think number line that extends all the way to the right as far as it can go --infinity--and all the way to the left toward the negative numbers as far as it can go--negative infinity.

Voila!

"I do not get the lion and bear reference,"

Yeah........you're not the only one.

(cricket sounds)

Every so often I make an attempt at a joke that is very esoteric and extremey egocentric. I think it is hilarious, but alas, I laugh alone..

So sorry....on a lighter note, thanks for the wiki reference!

We'll I'm laughing now, 'Neato! Crickets! LOL! You're totally cracking me up!

And Dottie got it. So I figure I'm the problem with this one, not you!

Well, I think Dottie was jumping in to save my butt, she didn't want me to be embarrassed.

TOO LATE!

So kind though, don't you think?

Must...........find bed........brain shutting down.......fingers typing...trying to supercede executive funtion.............

You misspelled "function" there, so I think you went one post too far for your brain...

:p

I should shut up and shut down, too. G'night, 'Neato.

There are different levels of infinity. That is for sure.

A simple way to get to infinity is the set of all numbers N+1. For any number I can name a number bigger by adding 1. This is a very small infinity. But its much bigger than all the stars in the universe.

An intermediate set is the set of all numbers derived by a set of functions where 1/N^K where k is all the numbers from 1..N.

Then there are the numbers from the set of ALL functions that are continous, which is also infinite.

In each above case, you can show that each set is infinitely larger than the other.

And it gets even more interesting than that.

It gives me vertigo when I think about it.

LMom and Austin are right that infinities come in different sizes (different "cardinalities"). One fun fact, which corresponds to the fact that (for a given cardinality) infinity plus infinity equals infinity is this: the set of all the even numbers is exactly as large as the set of all the odd numbers. Furthermore, each of these is exactly as large as the set of all the integers. You can tell that the evens are the same size as the odds by lining them up (putting them in "one-to-one correspondence"). Across from 1 put 2, across from 3 put 4, across from 5 put 6, and so on. Since it never happens that you have an odd number that has no even pair (or vice-versa), you've proven that the two sets have the same number of members. Then you can do this with either evens or odds on one side and all the integers on the other. It's one of the weird paradoxes of infinite sets that there are as many even numbers as there are integers.

But not all infinite sets are the same size. Georg Cantor, in the late 19th c., used the notion of one-to-one correspondence to prove that there are more real numbers than integers. It's called Cantor's diagonal argument. It's a pretty simple argument - many of the mathy kids will be able to understand it. What's neat is that it's not known whether there are any sets that are bigger than the natural numbers but smaller than the reals. Cantor hypothesized that there was no set whose size is strictly between that of the integers and that of the reals. This was called the Continuum Hypothesis (abbreviated CH, and referring to the fact that the set of reals form a continuum). In 1940 Goedel showed that using the standard axioms of set theory CH cannot be proved. Then in 1963 Paul Cohen proved that using those same standard axioms CH cannot be disproved. So CH is said to be "independent" of the standard axioms of set theory. One of the things that set theorist do is to look for ways to augment the existing axioms of set theory that allow us to decide the truth of otherwise independent hypotheses.

Contemporary set theory is a very hoary subject, and I'm at best someone who enjoys watching from the sidelines. But the introduction to the problems is very recent - starting with Cantor in the late 19th c. - and the moves made in the first half century or so are all pretty understandable. Anyone with mathy kids might find it an interesting project to pursue.

BB

Interestingly, the rational numbers are countably infinite as well.

Mathy kids may have fun finding a way to map the rational numbers onto the integers.

You guys are cracking me up... in a very positive way, mind you.

And we wonder why our kids are obsessed with numbers! Sheeeeesh.
The apple doesn't fall too far from the tree!

By complete synchronicity, I just got the following joke in an email...

"Aleph-null bottles of beer on the wall. Aleph-null bottles of beer.
Take one down pass it around. Aleph-null bottles of beer on the wall.
Aleph-null bottles of beer on the wall..."

(Only here could I share that...)

Is there a scratching head icon w/ confused expression on face?

aleph-null equals infinity.

Infinity minus one is still infinity.

Is that what you were confused about Dazed?

(I only really laughed hard at the email after reading the reference to aleph-null in a previous post. I read my email the first time fast enough that I didn't get the repeating 99 bottles of beer on the wall part of the joke!)

Okay, okay... maybe it wasn't that good of a joke! But I tried!!

I liked it.... I'm not sure what that means about me...

Dottie - I think I've been on that field trip!!!

ebeth - I laughed at your joke as well. So Cathy what does that mean about us?????

Great joke It's great to find a group of people who get it!

The Cantor's diagonal argument is beautiful. Math sure has lots of beauty.

I read it to my DH! What does THAT say about ME?!?!

Oops. Speaking about "what does that say to me", I was catching up on this thread just now and I re-read my post about Cantor and Goedel. Apologies for extreme geekiness. I'm afraid I hadn't had my morning coffee yet, so the filter between my brain and the keyboard hadn't kicked in.

BB

Nah, we're big fans of geekiness here. No filter required...unless it's the coffee filter and you're sharing with the rest of us!

Thanks, Kriston. Hereby offering coffee to all...

BB

Geeks R Us

Ha, ha! I asked my husband something about countably infinte sets and he said, "What message board is that? How does that topic come up in conversation, anyway?"

Blame it on the kids! It's their fault! (And for once, it really is!)

I take my coffee black, unless you've got a skim caramel macchiato with sugar free syrup back there, BB. An infinite refill would be nice, too!

Usually we drink virtual wine or virtual vodka in the back of 'Neato's closet when we're freaking out about our kids. An infinite cup of virtual coffee will make a nice, relaxed change!

Here is another for your kids.

I zero an even number or an odd number?

BTW -

GEB is a great book to get mathy kids. He ties together Bach, Escher, and Godel.

Feynman Lectures on Physics are real good, too.

And don't forget the Rubik's Cube!

Beware of Geeks baring gifts!

Hey, what's going on out here! I just came from the back of my closet. I was, sorting clothes.
hiccup.

Just kidding! Nothing to freak out about this whole summer! Hooray!

I don't recommend it, however, I wouldn't discourage it!

Mmmm...Baileys and coffee. Mmmm...

Now I have a craving!

There is an MIT open course on this. It looked very interesting. Sorry I don't have time to look for the URL, I have to go p/up dd from piano.

Summer