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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 s
by zw123456 3y ago
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.
- isitmadeofglass 3y agoIf I say someone had many of something, then I know for certain that they must have either an even amount or an odd amount. Same goes for few.
- zw123456 3y agoIt's an analogy, meant to show the similarities between two things in a limited way, to illustrate an idea. They do not have to be exactly the same in every way.
- Name_Chawps 3y agoThis is true until you introduce transfinite numbers.
- zw123456 3y agoThat might be a bit too advanced for a 6 year old perhaps.
- MengerSponge 3y ago6 year olds have an expert understanding in "I'm not touching you", so you might have a shot of teaching them
- gowld 3y agoOn the contrary, it's entirely natural. The technical definition is quite intuitive. "There are many infinities! The smallest one is bigger than all the counting numbers, so you can't count up to it, but it's out there! We call it omega. You can make bigger infinities too, like omega + 1!" Kids LOVE that, and it's good math too! (But gets tricky quickly, because addition of transfinite ordinals is not commutative, and standard transfinite ordinals don't allow subtraction) It's easy to draw as a "number tree" too: root / \ / \ 1,2,3,4... omega, omega+1,... https://en.wikipedia.org/wiki/Surreal_number#/media/File:Surreal_number_tree.svg https://en.wikipedia.org/wiki/Surreal_number#/media/File:Sur... (includes more numbers like rationals and reals and negatives and backwards counting from omega, but you can ignore those)
- bragr 3y ago>On the contrary, it's entirely natural. The technical definition is quite intuitive. https://xkcd.com/2501/ https://xkcd.com/2501/
- operator-name 3y agoTerminology and strict definitions aside, it is quite intuitive. A commenter below also pointers this out: > If you ask a child what comes after infinity, "Infinity + 1" is pretty much the default answer. Any kid who knows multiplication knows "Infinity + Infinity" is the same as "Infinity Times Two". The answer of "Infinity TIMES Infinity" is also popular for kids to say when they know a number bigger than their friend (who just proclaimed infinity is the largest number).
- tsoukase 3y agoMy 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
- Dylan16807 3y agoWell that fear is good because multiplication won't change the cardinality, you have to go exponential.
- smfjaw 3y agoThat effectively does make it exponential x * x === x^2
- ksarw 3y agoby going exponential, they mean 2^x; x^2 can still be the same "size" as x
- NobodyNada 3y agox^2 is not exponential; it's quadratic. 2^x is an example of an exponential function. The parent comment was alluding to the idea of set cardinality (https://en.wikipedia.org/wiki/Cardinality https://en.wikipedia.org/wiki/Cardinality). Two sets have the same cardinality if you can establish a bijection (a one-to-one mapping) between elements of one set and elements of the other. The set of all natural numbers is said to have a "countably infinite" cardinality. It turns out that for any countably infinite set S, the set S x S is also countably infinite (see Hilbert's hotel: https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Gra...). For example, the set of 2-tuples of natural numbers (1, 1), (1, 2), (1, 3), ..., (2, 1), (2, 2), ... is the same size as the set of natural numbers. So in this sense, "endless*endless = endless". Whereas the set of infinitely-long tuples of natural numbers is "uncountably infinite;" it has a cardinality greater than that of the set of natural numbers. Thus, "you have to go exponential"; i.e. "endless^endless".
- danwills 3y ago
- bmacho 3y agoThe 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.
- EA-3167 3y agoThe fallback metaphor I use in these situations or similar ones, "What's outside of the universe" for example, is the old, "What's North of the North Pole?" Then you explain that we can create questions and statements in our languages which don't have logical, mathematical or physical validity. Although we can often describe scientific and technical concepts in common languages, that's just a translation, the real language is math.
- gopher_space 3y agoCarlos Castaneda is at his most interesting when he wrestles with "what's outside of the universe" paradoxes since his informants seem like they're able to not only hold mutually exclusive concepts but exist in a relationship between them. They'd have an internally consistent idea about what's North of the North Pole and could explain it to you in terms you might understand. He's given me quite a bit to think about in regard to NULL and the assumptions I make around the concept, which is fascinating in itself because his books are hot garbage.
- justinator 3y agoI was so confused at your glowing review until the redemption of the last sentence.
- gopher_space 3y agoThe first one is basically "Fear and Loathing on the Campaign Trail '72" for anthro majors, and then he gets less focused somehow. He'd be my personal Kilgore Trout if we didn't have contemporary science fiction.
- analog31 3y agoI would start with a game: For any number, I can name a bigger number. For any collection with a certain number of things (such as n potatoes), I can always name a collection with more things, such as n+1 potatoes. "Infinity" is a word that we use for games like that.
- raldi 3y agoIs “up” an even or odd number of meters?
- kazinator 3y ago6 year old: But, sensei, what about Inf in the IEEE 754 spec? Sensei: Grasshopper, lecture over today.
- jjeaff 3y agoThe only thing that is a little off here to me is that I don't think there is mathematical notation for "many" or "few". And yet infinity does have mathematical notation and is used in some equations, no?