> It's the smallest number you can't count to
Funny. If explaining infinity to a kid had been my problem, I'd have tried hard to avoid calling infinity a number.
How to explain infinity to kids
81–90 of 139 posts
Re: How to explain infinity to kids
#82As a kid, I asked my mom if all numbers have a name, she said yes, and then I asked the obvious follow-up question: If there are infinite numbers, and all numbers have a name, then there must exist a number called door, another one named airplane, because at some point you would run out of numbery names, I don't remember what she said, but she didn't answer the question. That question was unresolved for me until rece…
If you're referring to real numbers, then virtually no real numbers have a name. If all real numbers had a name then you could order them alphabetically and put them in one-to-one correspondence with the natural numbers, which we know is impossible: https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument
That is something I hit uppon recently, when I tried to find a binary representation that could concievably represent all real numbers, given enough bits of data. I don't think I've ever seen such a practical application of countability and cardinality. Really interesting where this stuff manifests in the real world.
Re: How to explain infinity to kids
#83As a kid, I asked my mom if all numbers have a name, she said yes, and then I asked the obvious follow-up question: If there are infinite numbers, and all numbers have a name, then there must exist a number called door, another one named airplane, because at some point you would run out of numbery names, I don't remember what she said, but she didn't answer the question. That question was unresolved for me until rece…
The difference between "infinite" and "all possible" seems to be really unintuitive. The example I got to is that there are infinite even numbers, but not all natural numbers are even.
This also maniests itself when people talk about infinite universes. "If there are infinite universes, there has to be one in which X". Not necessarialy. Maybe only even universes exist and universes in which X is the case might all be odd universes.
Re: How to explain infinity to kids
#84Earlier quoted context omitted.
How long did that take you? Seems like it take at least a week.
A million seconds is over 11 days straight without stopping for sleep, food, or anything! I very much doubt that they actually did it.
If you count one a second, you're counting very slowly. Also, you can take breaks and pick it back up, making a note where you left off. I did it this way once, growing up.
Re: How to explain infinity to kids
#85As a kid, I asked my mom if all numbers have a name, she said yes, and then I asked the obvious follow-up question: If there are infinite numbers, and all numbers have a name, then there must exist a number called door, another one named airplane, because at some point you would run out of numbery names, I don't remember what she said, but she didn't answer the question. That question was unresolved for me until rece…
If you're referring to real numbers, then virtually no real numbers have a name. If all real numbers had a name then you could order them alphabetically and put them in one-to-one correspondence with the natural numbers, which we know is impossible: https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument
Does this apply if names are infinitely long?
Re: How to explain infinity to kids
#86Earlier quoted context omitted.
If you're referring to real numbers, then virtually no real numbers have a name. If all real numbers had a name then you could order them alphabetically and put them in one-to-one correspondence with the natural numbers, which we know is impossible: https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument
Does this apply if names are infinitely long?
No, then the names could just be the actual decimal representation of the number. But strings are in genereal considered to be finite.
Re: How to explain infinity to kids
#87Earlier quoted context omitted.
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.
Haha I counted to 32,000 once when I was around 7/8 years old. All I remember is it taking multiple days and my mouth was dry and sore. Props to counting to a million!
Re: How to explain infinity to kids
#88If we're going for useful lies to tide kids over, I quite like the explanation in the Postgres docs: > infinity (date, timestamp) later than all other time stamps I think you could tell a kid who wasn't quite ready for Aleph numbers that: > infinity is a useful made-up number that's bigger than all other numbers Which is useful when kids first hear about it, I guess. I think my first "practical" introduction to infin…
> infinity is a useful made-up number that's bigger than all other numbers I love the emphasis on this being a choice, and I wish this kind of thinking was taught more in math. So many math explanations act like these things are immutable facts of the universe, rather than human constructions. We lose some of the history and character of math when we teach it as law rather than invention. Zero is also a useful made-u…
I wish I could upvote this more. I encounter this very often in discourse. I extend this to logic and philosophy as well.
Without maintaining both the rigor and the creativity of reasoning, only a hollow shell remains.
Re: How to explain infinity to kids
#89Many mathematically-trained people fumble the infinity question because infinity is just a term or notation for something that is non-ambiguously defined. People tend to view infinity as a sort of weird, maybe even mystic, concept. Certainly the intuition behind it is useful for reasoning, but mathematically-speaking it's just a term for another formal definition.
Consider limits. One can say that a function converges to a certain value v when its input approaches infinity. This seems all subjective and mystic and non mathematically trained people would come up with all sorts of interpretation of that. But this just means that no matter how small a number ε you chose, then there exists a number x such that for any input greater than x, the function's output will be contained within v-ε and v+ε. That's it. It's as simple as that. There is no mystery to it, nor judgment. "Infinity" is just a name that is involved in such formal property.
Re: How to explain infinity to kids
#90As a kid, I asked my mom if all numbers have a name, she said yes, and then I asked the obvious follow-up question: If there are infinite numbers, and all numbers have a name, then there must exist a number called door, another one named airplane, because at some point you would run out of numbery names, I don't remember what she said, but she didn't answer the question. That question was unresolved for me until rece…
The difference between "infinite" and "all possible" seems to be really unintuitive. The example I got to is that there are infinite even numbers, but not all natural numbers are even. This also maniests itself when people talk about infinite universes. "If there are infinite universes, there has to be one in which X". Not necessarialy. Maybe only even universes exist and universes in which X is the case might all be…
I heard a really good interpretation of this recently.
In all these infinite universes, surely there's one where there's an ice cube in the middle of the sun, since that's one possible configuration of matter.
But no! There's no story that ends with an ice-cube in the middle of the sun. There's no sequence of events that could have resulted in that so it's not in the space of possible universes.