\infty = \lim _ { 0 \to \infty } x
that's how
How to explain infinity to kids
41–50 of 139 posts
Re: How to explain infinity to kids
#42Picking the first infinite ordinal as the infinity to explain to kids might not be the best choice for every kid, though. Oridnals are tricky. I am not too comfortable with them myself, and I say that as an adult with a degree in math! The thing is, this kind of infinity just doesn't come up that often when dealing with other objects in math. Even though, as Tom Lehrer sang, one can count up to infinity - or somewher…
Get a sheet of graph paper. Imagine that it goes on forever in 2 of the 4 directions. Name the intersection points in order -- left to right, top to bottom.
What's the name of the first point in the first row? 0
What's the name of the first point in the second row? \omega
How is that more complicated or less interesting than cardinals?
Re: How to explain infinity to kids
#43When my daughter was learning fractions, it was fun to use the infinity to discuss the real numbers between 0 to 1 by squeezing 1/ into them.
Re: How to explain infinity to kids
#44Why so complicated? Just ask them to do i++ and never stop. That is also infinity. (or in simpler words, imagine you have a table than you put one apple to it, then one again, amd again and again and never stop. And yes, they would also soon understand, that the table needs to be infinitly big) edit: of course it is about the sum of the process. they should imagine the pile of things or the number if you never stop a…
>Why so complicated? Because ifinity is complicated. >Just ask them to do i++ and never stop. That is also infinity. What, specifically, is infinity here? You are being vague here. Is it the process of counting up and never stopping? (that's the calculus infinity) The number you get in the end? (that's the infinite ordinal, but that is, as you noted, complicated ) The number of numbers ? (that's the cardinality of th…
I find explanations like this dangerously misleading, like Hilbert's Hotel and the Banach-Tarski paradox discussion talking about peas and suns. Infinity is not finite. Making it pretend-finite by making impossible analogies to finite physical objects instills fundamental misunderstanding of what finite and infinite means.
Re: How to explain infinity to kids
#45When my daughter was learning fractions, it was fun to use the infinity to discuss the real numbers between 0 to 1 by squeezing 1/ into them.
You don't even need the reals for that. Rationals is plenty.
Re: How to explain infinity to kids
#46> A professor of mine once said to me that all teaching was a process of lying, and then of replacing the lies with successively better approximations of the truth. Well put! I'm in the process of explaining my 3yo daughter different molecules (there are some cheap kits on Aliexpress) and cells and life on a micro scale and this description of moving from simple but inaccurate models to more complex and accurate is s…
>> all teaching was a process of lying > Well put! Shudder. Consider a thought experiment - a military briefing. A captain briefing generals. One must necessarily simplify. But imagine a briefing that is grossly incomplete, assortedly incorrect, very misleading, written without understanding and without mentioning and characterizing that lack, and pervasively incompetently bogus, and that captain later on the carpet…
> Shudder. I consider the "teaching is lying" meme to be vile.
Couldn't agree more. And when I read this in the article I also thought of high school chemistry even before I read your comment. I was put off chemistry in high school precisely because of its incoherence.
The best thing to do, as always, is to be honest. Tell your students that what you are teaching them is a simplification; a model that is useful at this level. Many will be satisfied with this answer and not want to go to a deeper level. But some children, those with a greater need for coherence and for things to make deep sense, will be reassured to know it's only a model and either wait for the deeper model to be taught or want to start exploring the deeper model at that time. Which is fine.
I found the approach taken by the author of this article quite patronising and rather distasteful.
Re: How to explain infinity to kids
#47I like the concept, but if I may editorialize, I feel the phrasing needs work. "The smallest number you can't count to" is a negative statement, which makes it confusing right off the bat. What do you mean, a number I can't count to? If I'm 8 years old this is like throwing a null pointer exception in my brain.
They might also take it literally. Like, they might think that infinity is less than a million because they know they couldn’t physically count to a million.
>couldn’t physically count to a million.
This is only because they/you haven't tried.
Source: counted to a million once.
Re: How to explain infinity to kids
#48Picking the first infinite ordinal as the infinity to explain to kids might not be the best choice for every kid, though. Oridnals are tricky. I am not too comfortable with them myself, and I say that as an adult with a degree in math! The thing is, this kind of infinity just doesn't come up that often when dealing with other objects in math. Even though, as Tom Lehrer sang, one can count up to infinity - or somewher…
Get a sheet of graph paper. Imagine that it goes on forever in 2 of the 4 directions. Name the intersection points in order -- left to right, top to bottom. What's the name of the first point in the first row? 0 What's the name of the first point in the second row? \omega How is that more complicated or less interesting than cardinals?
I guess I’m mixing up ordinals and cardinals but it seems odd that if you order the points differently ((0,0), (1,0), (0,1), (2,0), (1,1), (0,2), etc...)you never get to omega and cover all the same points.
Re: How to explain infinity to kids
#49Why so complicated? Just ask them to do i++ and never stop. That is also infinity. (or in simpler words, imagine you have a table than you put one apple to it, then one again, amd again and again and never stop. And yes, they would also soon understand, that the table needs to be infinitly big) edit: of course it is about the sum of the process. they should imagine the pile of things or the number if you never stop a…
> Just ask them to do i++ and never stop. That is also infinity.
Thinking back to that bug last week, where someone forgot that you can't just compare ever-incremented sequence numbers with 'x < y'... Maybe we don't want to encourage that idea :)
Re: How to explain infinity to kids
#50I don’t know if this would make any sense to kids, it certainly doesn’t to me.
If infinity + 1 exists, then that number would be infinity. It’d be more accurate to say that Infinity + 1 = NaN