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Is infinity an odd or even number? (2011)

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Re: Is infinity an odd or even number? (2011)

#81

Post by Sharlin »

remram wrote: post #3

Infinity 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 so simple after all.

Almost everything interesting in mathematics stems from a simple question: "How could we extend a concept to be more generally applicable?" Saying that infinity is not even or odd because it's not a number is like claiming that matrices can't be multiplied because they are not numbers.

Re: Is infinity an odd or even number? (2011)

#82

Post by bitL »

Cruncharoo wrote: post #76
bitL wrote: post #41

I really hate these mathematical technicalities spawned from material implication, chosen way of making a definition and vacuous truth - why can't we even consider some questions to be marked as non-sense/non-relevant like in relevance logic?

Not to be obtuse but isn't all of mathematics spawned from a chosen way of making a definition and vacuous truth?

Not really. One could argue some math is innate and we are just rediscovering it. See the disconnect between natural language and math which happened early 20th century because of material implication bringing vacuous truth, leading to "impedance mismatch". Medicine is still using counterfactuals precisely because of weirdness introduced by Russell in order to make all Boolean values defined for inference.

Re: Is infinity an odd or even number? (2011)

#83

Post by mlyle »

version_five wrote: post #75
warent wrote: post #10

In 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

Also my first thought. I assume he's writing this to other people who know what transfinite ordinals are (I don't understand the explanation) and would frame it differently with an actual kid. Even in context it's a hilarious quote though, I think it's possible this was on purpose

I think the big assumption that kids can't get "complicated" ideas is faulty.

Sure, they lack rigor, and often will just get the sketch of the idea.

And it's a lot more work to think about how to put things in the terms that a kid will understand given their knowledge so far.

But this idea? "Infinity plus one?!@" --- this is a conversation elementary school kids have on their own. Pulling it a little closer to a sane footing in ordinal analysis is not hard. Half of six year olds can handle it.

On the other hand, there's not a lot of obvious utility to teaching a six year old this particular concept early. On the gripping hand, there is a cost to keeping kids in a bubble where you don't talk about any big ideas (of whatever sort-- mathematical, philosophical, historical, linguistic) at all, or excessively dilute them to the point where they're meaningless.

Re: Is infinity an odd or even number? (2011)

#84

Post by LudwigNagasena »

bitL wrote: post #41

I really hate these mathematical technicalities spawned from material implication, chosen way of making a definition and vacuous truth - why can't we even consider some questions to be marked as non-sense/non-relevant like in relevance logic?

That has nothing to do with relevance logic. Someone has written a smart-ass answer about transfinite ordinals to a question about infinity; and people upvoted it for right or wrong reasons. To me personally the answer looks witty but misleading.

Re: Is infinity an odd or even number? (2011)

#85

Post by bombolo »

taneq wrote: post #56
irrational wrote: post #14

>To explain the idea to a child, I would focus on the principal idea: whether finite or infinite, a number is even when it can be divided into pairs. For finite sets, this is the same as the ability to divide the set into two sets of equal size, since one may consider the first element of each pair and the second element of each pair. The answer this quote came from is amazingly obtuse, but it does make me think that…

Infinities aren’t comparable for equality… are they?

Not if you aim to pass your exam.

Re: Is infinity an odd or even number? (2011)

#86

Post by lisper »

To explain to a six-year-old I would start by telling them that there are many different kinds of infinity, not just one. Some infinities are odd, others are even, and others are neither. It matters whether you are asking "how many" (cardinals) or "in what position" (ordinals). For regular finite numbers, cardinals and ordinals are (more or less) the same, but for infinities they behave differently. Then, if they want to get into the weeds, you can introduce them to transfinite ordinals, diagonalization, and all that fun stuff.

Re: Is infinity an odd or even number? (2011)

#87

Post by Georgelemental »

yamtaddle wrote: post #33
contravariant wrote: post #15

Earlier quoted context omitted.

Depends what you mean by decimal. Decimal is a system of notation, does it count as a decimal number if it cannot be written in decimal notation (in finite time)? if not then they are equal, if yes then there are more decimal numbers between 0 and 1 than integers.

I don't usually use that term, but I take it to mean "number you (may, and, if not using e.g. fractions, must) write using a decimal point" because that seems to always be what people intend by it. Everybody experienced writing irrational numbers using decimal notation in school, so those definitely count.

> Everybody experienced writing irrational numbers using decimal notation in school,

To be pedantic, we experienced writing approximations of these numbers in decimal arithmetic.

Re: Is infinity an odd or even number? (2011)

#88

Post by bombolo »

tobiasSoftware wrote: post #36
Eisenstein wrote: post #9

I want to know if there are more decimal numbers between 0 and 1 than there are integers between 0 and infinity.

There are, and it turns out that this is a significant mathematical concept. The integers between 0 and infinity are defined as "countably infinite". Other infinities are considered countably infinite, or the "same" infinity, if and only if you can arrange it in a list such that each item in the list pairs to an integer in our 0 to infinity list. So the set of even numbers is countably infinite because for every i th…

does decimal numbers mean fractions or real numbers?

If it means fractions only, they are countable.

Re: Is infinity an odd or even number? (2011)

#89

Post by MalcolmDwyer »

vmilner wrote: post #64
alexb_ wrote: post #12

Earlier quoted context omitted.

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).

Child: “Is 100 million the biggest number?” Teacher: “Well, there’s 100 million and one” Child: “I was pretty close then!”

https://m.youtube.com/watch?v=9P2ROAbQZYw

Twenty-four is the highest number! That's it. Let it go.

Re: Is infinity an odd or even number? (2011)

#90

Post by bombolo »

yamtaddle wrote: post #69
xigoi wrote: post #65

Earlier quoted context omitted.

The correct mathematical term is “real number”.

Yes, but you'll see "decimal" more in the wild, and that's what people mean by it. "You write it with a decimal point", and they do usually mean to include the irrationals. So, yes, real numbers, but the reasoning behind their usage is "you write it with a decimal point". I'd bet more people understand "decimal number" used in that sense, than understand "real number".

i've never seen an irrational number written in digits in my whole life. Have you?????

I've seen them expressed as letters or formule

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