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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)

#301

Post by bragr »

gowld wrote: post #290
zw123456 wrote: post #247

Earlier quoted context omitted.

That might be a bit too advanced for a 6 year old perhaps.

On 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, a…

>On the contrary, it's entirely natural. The technical definition is quite intuitive.

https://xkcd.com/2501/

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

#303

Post by froh »

logifail wrote: post #227
areyousure wrote: post #147

Earlier quoted context omitted.

> Presumably this person has no experience with 6 year olds? In case anyone is curious, this person has experience teaching children mathematics. For example, on his blog, we have http://jdh.hamkins.org/math-for-six-year-olds/ http://jdh.hamkins.org/math-for-seven-year-olds-graph-colori... http://jdh.hamkins.org/math-for-eight-year-olds/ http://jdh.hamkins.org/math-for-nine-year-olds-fold-punch-cu... The most recent…

> this person has experience teaching children mathematics Just as a FYI, there are plenty of countries in Europe where many 6 year-olds are still in kindergarten not at school, as a result they most likely have not have properly started learning numbers or reading and writing. https://www.statista.com/chart/13378/when-do-children-start-...

unless the kindergarten is playfully toying with numbers already, usually with no obligation but as an enrichment for those kids who love such activities.

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

#304

Post by ilyt »

areyousure wrote: post #147
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

> Presumably this person has no experience with 6 year olds? In case anyone is curious, this person has experience teaching children mathematics. For example, on his blog, we have http://jdh.hamkins.org/math-for-six-year-olds/ http://jdh.hamkins.org/math-for-seven-year-olds-graph-colori... http://jdh.hamkins.org/math-for-eight-year-olds/ http://jdh.hamkins.org/math-for-nine-year-olds-fold-punch-cu... The most recent…

Do we have statistics on how many pupils end up hating/loving math after that ?

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

#305

Post by bmacho »

gowld wrote: post #291
bmacho wrote: post #255

Earlier quoted context omitted.

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.

The OP clearly explains why the question is meaningful.

The question is not meaningful as is.

If you try hard enough, you can find similar questions, that do type-check. You can talk with 6yo children about them if you want. Still, I stand with my answer. I would say this (also I think this is the best thing to say/I am capable of).

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

#306

Post by crazygringo »

skulk wrote: post #163
crazygringo wrote: post #159

Earlier quoted context omitted.

OK, so I guess I'm just understanding that mathematicians arbitrarily decided to prioritize "even" over "odd"? Because as I stated in another comment, you could just as easily say odd cardinality exists if you can find two subsets with the same cardinality and there's one element left over, and otherwise we call it even. So at the end of the day, what you're saying is that ultimately infinity would be even just becau…

well, if you claim omega is odd, are you willing to claim omega + 1 is even? There is no ordinal B such that 2 * B is omega + 1, so it fails that definition. So you have to say omega is odd and omega + 1 is also odd, which is... odd.

But that "oddness" is precisely my whole point.

I'm arguing that because it's just as easy to say that omega is odd as to say that it's even, that the whole concept breaks down and loses and all meaning.

Because if you want to divide omega + 1 in half to show that it's even, we can do that. If we denote the set element inside of the "1" of "+ 1" by the symbol "a", then we can write out:

  [1, 3, 5, 7, ...]
  [a, 2, 4, 6, ...]
We can infinitely extend this 1-1 correspondence between these two disjoint subsets, so omega + 1 is evenly divisible. (Or, again, it can also be odd if you choose to arrange the elements differently.)

But I'm not saying that this is useful or interesting. My whole point is that it's not because even/odd is not meaningful at all for transfinite numbers, because they're just as odd as even. That in the same way there's no utility in attempting to decide whether the decimal 2.7 is odd or even, there's similarly no utility in defining omega as odd or even (or omega + 1).

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

#307

Post by chrisoverzero »

FabHK wrote: post #101
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).

> Any kid who knows multiplication knows "Infinity + Infinity" is the same as "Infinity Times Two". Or is it "Two Times Infinity"? (Hint: It isn't, because "Two Times Infinity" = "Infinity", while "Infinity Times Two" = "Infinity + Infinity". Not sure every kid knows that.)

I think you have that backwards. “Two times infinity” is “infinity, two times” or “infinity, twice,” which maps to Infinity + Infinity. “Infinity times two” is 2 + 2 + 2 + 2 + 2… forever.

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

#308

Post by jdkee »

short_sells_poo wrote: post #299
thriftwy wrote: post #267

Earlier quoted context omitted.

Infinite is just a fancy word for endless, anyway.

Not necessarily:) A circle is endless, and yet certainly isn't infinite.

A circle is made up of an uncountably infinite set of points.

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

#309

Post by ForOldHack »

ForOldHack wrote: post #269

Ahh, the mis-uses of infinity again. Infinity, is both simply because inf+1 = inf, so if infinity is odd, then infinity + 1 is even, which equals infinity which is then odd. Think of sets. Inf and -inf are in both sets. You can prove this with deltas and epsilons, but that is beyond the scope of explaining it to 6 year olds.

There are twin primes, and the number of twin primes is infinite, so now, the number of twin primes should be even... because by definition they always are. Also the number of primes is infinite, so there is both a even number of primes, and an odd number of primes.

Infinite sets are indivisible, and also have infinite magnitude. i.e. you cannot sub divide them into anything, and loose its infinite property, you also cannot multiply them, and change the infinite property,

so, If someone says Infinity = 1/12 its useful, but tricky.

if you multiply both sides of that you get infinity * infinity = 1/12 * infinity. i.e. it reduces to infinity = infinity.

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