Well its not a natural number or real, its a concept entailing all odd and even numbers.
Unless this is some sort of trick question or I am missong something.
Is infinity an odd or even number? (2011)
211–220 of 398 posts
Re: Is infinity an odd or even number? (2011)
#212In my experience with children, one of the easiest-to-grasp concepts of infinity is provided by the transfinite ordinals, since it can be viewed as a continuation of the usual counting manner of children, but proceeding into the transfinite: 1,2,3,⋯,ω,ω+1,ω+2,⋯,ω+ω=ω⋅2,ω⋅2+1,⋯,ω⋅3,⋯,ω2,ω2+1,⋯,ω2+ω,⋯⋯ Presumably this person has no experience with 6 year olds? This explanation is horrendous haha
> In my experience with children, one of the easiest-to-grasp concepts of infinity is provided by the transfinite ordinals
Things people say on HN :)
Re: Is infinity an odd or even number? (2011)
#213Infinity is a direction.
Re: Is infinity an odd or even number? (2011)
#214Infinity is not a number. If you want to extend even/odd to it, you can pick whatever you want.
There's always someone who sees a question in a submission title and feels the need to comment simply to answer said question in the most boring, banal, and least insightful way possible. Most people realize that if an article that poses a seemingly-simple question makes it to HN frontpage, there's almost certainly some unexpected, interesting, and/or insightful discussion there that reveals that the question wasn't…
I am not preventing the discussion or claiming that you shouldn't extend this concept, just objecting to the way to question is formulated ("is infinity an odd or even number"). The stackexchange comments agree with me, and do this extension by pointing out reasons it would be useful to pick one or the other, but I found it important to point out this caveat that there is no logical answer (in terms of numbers) and whatever you pick would be an extension, not a conclusion.
Nowhere in my comment do I say that this is a silly submission or suggest that it shouldn't be in the front page.
Re: Is infinity an odd or even number? (2011)
#215Earlier quoted context omitted.
What? Where does that follow from?
It follows from the way addition is defined on top of set theory. "a + b" is implemented as "increment a (the set that represents a) b times". A number is represented in set theory as a set that contains all of the numbers before it. 0, 1, 2 is {}, {{}}, {{} {{}}}... SO! If you start with a finite "a" and increment it infinite times, you still have infinity; you haven't broken out. But if you start with Infinity, the…
Is addition defined _by_ set theory, or is set theory one way of defining addition? If it's the later, then there could be other ways of defining addition that don't have the same results for infinity (because our math system doesn't really "work" for infinity, or 0, depending on the circumstances).
I am in no way a mathematician. My question about the definition of addition as it relates to set theory is just that; a question.
Re: Is infinity an odd or even number? (2011)
#216Is the last digit of Pi odd or even?
Re: Is infinity an odd or even number? (2011)
#217Is the last digit of Pi odd or even?
Trick question. Pi is irrational and does not have a last digit.
Re: Is infinity an odd or even number? (2011)
#218npm i is-even const isEven = require("is-even"); console.log(isEven(Infinity)); TypeError: is-odd expects a number.
I read the title and I sarcastically thought "ask JavaScript!"
Your comment didn't disappoint. Importing the is-even package is the cherry on top.
Re: Is infinity an odd or even number? (2011)
#219npm i is-even const isEven = require("is-even"); console.log(isEven(Infinity)); TypeError: is-odd expects a number.
I read the title and I sarcastically thought "ask JavaScript!" Your comment didn't disappoint. Importing the is-even package is the cherry on top.
The amazing thing is that the is-even package depends on the is-odd package.
I would have thought the reverse, but ¯\_(ツ)_/¯
Re: Is infinity an odd or even number? (2011)
#220In my experience with children, one of the easiest-to-grasp concepts of infinity is provided by the transfinite ordinals, since it can be viewed as a continuation of the usual counting manner of children, but proceeding into the transfinite: 1,2,3,⋯,ω,ω+1,ω+2,⋯,ω+ω=ω⋅2,ω⋅2+1,⋯,ω⋅3,⋯,ω2,ω2+1,⋯,ω2+ω,⋯⋯ Presumably this person has no experience with 6 year olds? This explanation is horrendous haha
No it isn't. 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).
> If you ask a child what comes after infinity, "Infinity + 1" is pretty much the default answer
(Full disclosure: have three children and plenty of STEM in the family)
I'm not sure that's the _default_ answer, of course one might easily get that answer if at least one parent has a STEM background.
Schools don't teach about infinity to young children. A pity, really.