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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)

#101

Post by FabHK »

alexb_ wrote: post #12
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

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.)

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

#104

Post by [deleted] »

aaronharnly wrote: post #99
hammyhavoc wrote: post #67

Earlier quoted context omitted.

I had it explained at a very early age as "three lots of three", and to imagine it like three boxes of three ice-creams. Treating the multiplication symbol as one would to indicate quantity in a list, thus calculating how many ice-creams there are.

Found the Brit! As an American I’d never heard the “lots of __” phrasing until I watched Numberblocks (a British show) with my kid…

[deleted]

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

#105

Post by FabHK »

jameshart wrote: post #94
yamtaddle wrote: post #33

Earlier quoted context omitted.

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.

Nobody ever finished writing an irrational number in school.

sqrt(2)

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

#106

Post by SideburnsOfDoom »

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…

> it does make me think that infinity must be even since infinity can be divided into 2 pairs, each of which is of equal size since both are infinity.

This is true,

but the same is true of (infinity - 1)

Therefor infinity must also be odd.

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

#107

Post by gregschlom »

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

In the comments of the answer the author says they have a 4 and a 9 year old:

"Bill, despite your emphatic comments, I know for a fact that counting into the ordinals is something that children can easily learn. I have two young children (ages 4 and 9), who are happy to discuss ℵα for small ordinals α---although my daughter's pronunciation sounds more like Olive0, Olive1---and my son can count up to small countably infinite ordinals. The pattern below ωω is not difficult to grasp. Below ω2, it is rather like counting to 100, since the numbers have the form ω⋅n+k, essentially two digits"

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

#108

Post by cubefox »

w0mbat wrote: post #79

Infinity is not a number, it's the absence of a limit.

Yeah. Though the defenders of transfinite (ordinal and cardinal) numbers do in fact assert that there are many infinite numbers, such as aleph zero or omega. They are just usually somewhat embarrassed about this and therefore only talk about "ordinals" or "cardinals". It's like trying to hide that you drink beer by saying you merely drink lagers and ales.
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