My 6 year old daughter just asked me....

[Lazy-Commuter]

Our five year old is doing numbers at school. As we talked about our day at work / school over tea the other night she asked (with that great honest sincerity that kids have): "What's the last number?"

Priceless.

That question from Little-LC as I was putting her to bed a few years ago got me in all sorts of difficulty. I initially answered ..

Infinity?

.. which led to the "what about Infinity plus 1" question, so then I had to try to explain that it's not really a number .. more a concept. Then we ended up in the world of different infinities: the set of integers (whole numbers: 1, 2, 3, 4, etc) is infinite, for example, but so is the set of real numbers (decimals: 1.01, 1.02, 1.03 with however many zeroes after the point you care to fancy) and of course that second set is bigger than the first set. All this to a (then) 6yo. What was I doing?! Floundering, that's what.

So I branched out into Googol (10^100 or 1 with 100 zeroes - thanks, Fnaar) and then GoogolPlex (10^Googol or 1 with a Googol zeroes) and then, thankfully, it was Mrs-LC's turn to kiss her goodnight.

Little-LC had trouble sleeping that night. Though she does still remember the symbol for infinity (∞) and then Littlest-LC wrote an 8 sideways whilst doing some maths homework the other week and it all started up again, but with both of them this time.

 

[red_tom]

Great stuff there! Reminds me of being taught maths at an early age by my brothers. If you want really big, how about Graham's number.

Indeed, it is not possible, given the limitations of our universe, to denote Graham's number, or any reasonable approximation of it, in a conventional system of numeration.

 

[Lazy-Commuter]

Great stuff there! Reminds me of being taught maths at an early age by my borthers. If you want really big, how about Graham's number.

Indeed, it is not possible, given the limitations of our universe, to denote Graham's number, or any reasonable approximation of it, in a conventional system of numeration.

I'd never heard of that one .. but my brain melted about 3 paragraphs in to the explanation!!

 

[got-to-get-fit]

So I branched out into Googol (10^100 or 1 with 100 zeroes - thanks, Fnaar) and then GoogolPlex (10^Googol or 1 with a Googol zeroes)

+1

 

[Fnaar]

Googol pffft. Try a Googolplex.

Now that's just silly A googolplex and one

 

[ChrisKH]

Ahh, but is infinity actually a number?

Indeed. My six year old said it was made up and you could never get to it. Smart boy. I've shown him the mathematical symbol and told him to introduce it as a concept at school. Just to keep his teacher on her toes.

 

[dellzeqq]

Indeed. My six year old said it was made up and you could never get to it. Smart boy. I've shown him the mathematical symbol and told him to introduce it as a concept at school. Just to keep his teacher on her toes.

clearly the kind of parent who demands to know why his offspring can't use the log tables that served him so well...........

 

[ChrisKH]

clearly the kind of parent who demands to know why his offspring can't use the log tables that served him so well...........

Heh heh, haven't used log tables since A-level maths. This suggestion has opened up a whole new area of learning for Junior2. I'll have to re-teach myself what I needed them for now. Maybe just dig one out and put it in his school book bag.

 

[Sh4rkyBloke]

I think I'm in for some fun in years to come when answering such questions as these, as I tend to give the logical/correct answer rather than any flannel.

Example, my 5 year old asked me recently if you would die if you breathed underwater (I was trying to explain how/why I went underwater in the bath - i.e. holding my breath) to which I replied...

"Well, technically no. If you have air with you and are able to breathe it (i.e. SCUBA which she knows about as I used to do it) then you will be fine (ignoring all other factors such as depth / rate of ascent etc.). However, if you just try to breath the water then yes, you *could* die."

My wife rolled her eyes and asked why I just didn't say "Yes" as she know thinks that said 5 year old will try to breathe in when she goes underwater...

Don't see the point in flannelling them - eldest has always been taught to be careful around roads/cars as if one hits you then you'd probably be dead (although Death as a concept is another whole can of worms to open!)... as a consequence she has good awareness of traffic and does not mess about by roads and we've no concerns about her running into the road (like some parents we see grabbing their kids when they approach within spitting distance of a road).

 

[Lazy-Commuter]

I think I'm in for some fun in years to come when answering such questions as these, as I tend to give the logical/correct answer rather than any flannel.

<snip>

Absolutely agree. And Little-LC has been blessed / cursed * with an insatiable curiousity which I do my best to deal with. We have some great question and answer sessions: a couple of years ago, we found a bit of paper in her bedroom with a list of questions she'd obviously thought of to ask me written on it. All the ones I'd already answered were ticked off.

The earliest time I ran into it was when she was not quite three and we were out quite late one night in September and the sun was just setting. There was one of those hazy skies where you could quite easily (and safely!) see the disk of the sun which was red. So she asked why it was red.

I told her it was 'cos the sun was low in the sky but she wasn't having that as enough of answer, so I tried the "Calvin's dad" approach (from the Calvin and Hobbes cartoon strips) and said it was because the sun was puffed out after running all the way across the sky all day.

But "that's just silly, daddy" so I had to go for the whole scattering of wavelengths of light thing. That got me the reply of, "daddy <pause> you have to say things so I know what you're saying. I'm only little and I don't know what you're saying when you say it like that".

Mrs-LC gave a shaved down explanation at that point which seemed to satisfy.

* delete as applicable

 

[marinyork]

If one wants to explain opposites of opposites the best thing is to explain about inverses in a number of situations. Less formally you could go for geometrical interpretations to show that sometimes the "opposite" of the opposite is what you had originally and sometimes it is anticommutative. You can even get onto pseudovectors which you can take as high as you like and have a profound affect on reality.

 

[Lazy-Commuter]

If one wants to explain opposites of opposites the best thing is to explain about inverses in a number of situations. Less formally you could go for geometrical interpretations to show that sometimes the "opposite" of the opposite is what you had originally and sometimes it is anticommutative. You can even get onto pseudovectors which you can take as high as you like and have a profound affect on reality.

.. but you have to say it so I know what you're saying.

 

[marinyork]

Google abelian group. I can't write TeX in this forum.

As for geometric interpretations. Matrix operations are not always commutative and you can represent things like rotations and reflections as matrices. It follows that there will be matrices that when multiplied together are not commutative e.g. a rotation by a right angle followed by a reflection in the x-axis is not the same as a reflection in the x-axis followed by the same rotation.

If you go on wikipedia's article on the dihedral group and scroll down to D2 and D4 where there is a picture of Fs on the right, this explains it quite well with the pictures of the F.

 

[Lazy-Commuter]

Sorry, marinyork, I was making a (weak) joke on my earlier post ..

 

[marinyork]

I hope you know Georg Cantor went mad