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Here's one that gets me: what's the sign of infinity? What do I mean? 1/d retains the sign of d across all finite and infinitesimal values. 1/ε = +∞, 1/-ε = -∞ So what about 1/0? Neutral infinity.
Or if you must, you do that thing where you pick the positive option à la √
The way I would explain it to a 6 year old would be like this: Infinity isn't a number really, it's a concept, like the word many or the word few. If someone says they have many of something, you don't think is that odd or even you just know they have a lot of it. Infinity is kind of like that, it explains the idea of things going on forever, not an exact quantity of things like the number 10 or 11.
PS: they seem to _know_ that endless*endless > endless but do not dare to admit it
Ah, StackExchange! The answer that says "Here is a simple example that has some hope of being comprehensible to a 6-year-old." and then begins "Consider the ring of polynomial functions with integer coefficients, ..." gets upvoted tens of times. Even the answer that uses "numerocity", "refined cardinality", and "logarithm" as the explanation to a 6-year-old gets upvoted. The answer, https://math.stackexchange.com/a/4…
A six year old can absolutely grasp that even means "being able to be split into two equally sized piles" where equally sized means each thing in the left pile can be matched to something in the right. 6 apples is even because you can split them into 3 and 3.
Then for infinity you separate them into the even and odd numbers, boom. Infinity is even.
Saying "infinity isn't a number", to me, is so much worse an answer because it's not satisfying. Because both you and the 6 year old know that isn't right. The 6 year old is grasping at a bigger concept but doesn't have the words.
The way I would explain it to a 6 year old would be like this: Infinity isn't a number really, it's a concept, like the word many or the word few. If someone says they have many of something, you don't think is that odd or even you just know they have a lot of it. Infinity is kind of like that, it explains the idea of things going on forever, not an exact quantity of things like the number 10 or 11.
There are natural numbers, like 0,1,2 and so on. Natural numbers can be odd or even. There is no such natural number as infinity. Therefore the question if 'infinity' is odd or even is meaningless. It does not even type-check.
In math people like well-formed questions, and generally don't like ill-formed questions.
The way I would explain it to a 6 year old would be like this: Infinity isn't a number really, it's a concept, like the word many or the word few. If someone says they have many of something, you don't think is that odd or even you just know they have a lot of it. Infinity is kind of like that, it explains the idea of things going on forever, not an exact quantity of things like the number 10 or 11.
My 6 and 7 yo's call infinity the "endless number". Well, at least it is a NaN number :) PS: they seem to _know_ that endless*endless > endless but do not dare to admit it
The way I would explain it to a 6 year old would be like this: Infinity isn't a number really, it's a concept, like the word many or the word few. If someone says they have many of something, you don't think is that odd or even you just know they have a lot of it. Infinity is kind of like that, it explains the idea of things going on forever, not an exact quantity of things like the number 10 or 11.
The way I would explain it to a 6 year old would be like this: There are natural numbers, like 0,1,2 and so on. Natural numbers can be odd or even. There is no such natural number as infinity. Therefore the question if 'infinity' is odd or even is meaningless. It does not even type-check. In math people like well-formed questions, and generally don't like ill-formed questions.
Earlier quoted context omitted.
I thought that most of us learn at an early age, as a result of this kind of exchange, that "infinity" is not "the biggest number" or even a number at all, as far as the ordinary notion of "number" goes.
No math instruction I had ever discussed infinity with any rigor until calculus -- and even then, it was only infinity as a limit. Infinity as a concept was brushed off in the same way that the square root of negative one was brushed off until we were actually taught about it.
Or put another way, "what's ∞ + 1" basically invites the non-answer "that's not a well-formed question" whereas "what's ω + 1" gives you a whole intellectual thread to pull on.
Here's one that gets me: what's the sign of infinity? What do I mean? 1/d retains the sign of d across all finite and infinitesimal values. 1/ε = +∞, 1/-ε = -∞ So what about 1/0? Neutral infinity.
1 / 0 = ±∞ Or if you must, you do that thing where you pick the positive option à la √
But there's no ambiguity here - those signs that you're suggesting popped out of nowhere.