# Teaching the Concept of Infinity to Children.

I was recently out with the family and we left it up to the children where we ate lunch (11 and 9 years old). They couldn't agree and were going back and forth calling each other names. This ultimately lead to the age old tradition of one kid saying to the other "You're stupid times infinity". Afterwards, the 9 year old asked me what infinity was and I attempted to explain it to him in the way that I understood it as a kid through audio and visual feedback examples.

Audio feedback (simplified): the loop created by a microphone and amplifier when the microphone picks up the sound coming out of the amp.

The example I used for visual feedback was the loop created by two mirrors. This was the one that really resonated with the kid and seemed to help them understand a bit better that infinity was without a limit (or endless as the kid understood it).

What I'm wondering, is if these are viable real life examples of infinity. If so, are there any more that could be used?

I read through a few of the other questions on infinity here on MSE and they didn't quite talk about infinity in this sense. This also got me to think that perhaps this is intentional and that we cannot have a legit real life example of infinity.

• As a kid, when I would look at the night sky, I used to think that if I could fly out far enough into space, I would eventually reach a black wall. I had no concept of infinity. Now, when I look at the night sky, I pretend that if I were to fly out, I would never reach any walls. To me, that is infinity (regardless of whether or not it is an accurate real life example!). Commented Aug 7, 2014 at 2:40
• @WillJagy That is where I got the idea of calling myself a Mathemagician (despite not being a magician). Just that to the average person it seems like I do magic with numbers. Commented Aug 7, 2014 at 2:48
• Since they can simulate nonphysical geometries, video games might be a good touchpoint. A specific example (which is basically the same as The Phantom Tollbooth's) is from Super Mario 64: Unless you've made enough progress, a staircase near the end will just continue on endlessly without end, and you'll return to the start quickly upon turning around. (So I guess one could be a bit absurd and say: "Infinity is never being able to fight Bowser.") Commented Aug 7, 2014 at 3:28
• Take them on a long drive. The phrase 'are we there yet' will be repeated an infinite number of times. Commented Aug 7, 2014 at 4:46
• Perhaps better suited to matheducators.stackexchange.com ?
– lhf
Commented Aug 8, 2014 at 12:14

To tell someone what infinity ... Take a sheet of $A4$ paper and divide it into two halves. Now take one of the halves and divide it again. Repeat this step indefinitely. Here ask the question 'Will this process finish?'.

• actually, the process will finish at some point.. There are only finite number of atoms in that sheet Commented May 16, 2015 at 6:08
• @typetraitor: And that's quite aside from the fact that eventually the child will pick up a piece of paper and actually try to fold it a lot, and will soon find that after about seven folds it becomes more-or-less impossible (at the very least with human hands alone). Commented Dec 23, 2016 at 19:37
• @typetraitor an atom doesn't have a half side !!!? Commented Oct 3, 2017 at 18:38

I teach infinity by using the number line. Tell the child that each point on the line represents a number, where the numbers are arranged such that the larger numbers are on the right. Then tell them that infinity is the number (the point) that is the largest (the farthest to the right). If they're smart, they'll see that no such number (or point) exists. Infinity is a concept with no counterpart number (or point).

• By the way, in the future, you might want to ask questions like this at Mathematics Educators Stack Exchange.
– JRN
Commented Aug 7, 2014 at 3:21
• Of course, I'm limiting the discussion to real numbers only (and not, say, the extended real numbers). By teaching infinity as the point farthest to the right on the number line, the child should see that questions such as "What is infinity plus one?" are meaningless, because "by definition," there is no number greater than (no point to the right of) infinity.
– JRN
Commented Aug 7, 2014 at 3:23
• And what happens when they actually draw a line (or look at the line you've drawn) and see that it has an end? Your answer merely relocates the problem to that of helping the child to conceive of an indefinitely long line. Commented Dec 23, 2016 at 19:47

Infinity and Me is a children's book that literally and figuratively illustrates the concept of infinity, in a way that is accessible to all ages.