This thread almost reads like parody to me. It perfectly encapsulates the Stack Exchange experience in that when a question is clearly asked by a beginner in a subject, they are likely to get responses only decipherable by experts, or at least people who know enough to not be asking that question.
Is infinity an odd or even number? (2011)
191–200 of 398 posts
Re: Is infinity an odd or even number? (2011)
#192In 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
I explained basically this to my 4 year old nephew recently. He wanted to count to infinity. I asked him what is the biggest problem with counting to infinity? It's too slow. I said ok let's take bigger steps. We counted by 2's then 10's then hundreds and millions and then zillions and other ridiculous superlative numbers. It doesn't really matter because everything is still too slow. So then we said ok lets make up…
He adds one more and the dog freezes at the event horizon of a black hole.
Re: Is infinity an odd or even number? (2011)
#193Earlier quoted context omitted.
Some do, yes. If they have an aptitude for basic sums then pointing out that 3 x 3 is the same as 3 + 3 + 3 sets them down the right path ...
The technique used by the Oregon public school system in the 80s went something like "Hand the child a 10x10 grid of numbers, then tell them, absent of any other context, that they must be memorized." I like your way better.
Ontario's 1990s curriculum was pretty awesome. The idea of dimension and sets were both introduced simultaneously and joined, using multiplication. Started in the 2nd grade and they just kept elaborating. Number lines and groups of items. (Tied it into geometry, too. Square numbers came up by at least 4th grade.) What is 3 x 3 but moving 3 units, 3 times in one dimension? Now, memorize these tables up to 12 x 12, you won't always have a calculator at hand.
Re: Is infinity an odd or even number? (2011)
#194Earlier quoted context omitted.
> 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.
The concept of "infinity - 1" doesn't exist. Subtraction isn't defined for ordinals. Furthermore even if you try to define it, it doesn't work for limit ordinals. If you are thinking about the difference between [0,1,2,3,…] and 0, [1,2,3,4,…] Then I regret to inform you the former is omega and the latter is 1+omega which is the same as omega. In other words attempting to subtract one from infinity by removing from th…
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Re: Is infinity an odd or even number? (2011)
#195So there seems like a glaring hole in the answer, but maybe I'm missing something. Because: > It is easy to prove from this definition by transfinite recursion that the ordinals come in an alternating even/odd pattern, and that every limit ordinal (and hence every infinite cardinal) is even. Sure, if we use the natural numbers and start at 1, then we can group: [1, 2], [3, 4], [5, 6], ... and prove infinity is even.…
> we can...prove infinity is even....and prove infinity is odd...
> maybe I'm missing something
The answer said:
> the usual definition is that an ordinal number 𝛼 is even if... Otherwise, it is odd.
In other words, if a number could be proved to be even, it is even. If not, it is odd.
Using their definition, there is no such thing as "proving a number is odd". You'd have to do it by failing to prove it's evenness. In the case of infinity, because we can successfully prove evenness, it's even and not odd.
Re: Is infinity an odd or even number? (2011)
#196Earlier quoted context omitted.
You can uniquely map all rationals onto the natural numbers, thus they are of the same quantity. That doesn't work for all real numbers thou.
Maybe this is misguided cheat, but couldn't you map any real number (between 0 and 1) to a natural number by mirroring the decimal digits across the decimal point. So 0.123 -> 321, but also sqrt(2)/2 -> ?601707 where ? is the rest of the decimal representation. This creates infinitely large numbers, but it's still a 1-to-1 mapping.
Unfortunately, numbers with infinitely many digits are not natural numbers. You cannot count to ?601707, even with an infinite amount of time.
Re: Is infinity an odd or even number? (2011)
#197Earlier quoted context omitted.
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
Never. Never in school? It's totally normal in the US, it's the reason as many people know that π starts "3.14" as do.
Yes never, not in school, not in analysis, and certainly not in numerical analysis.
You've proved my point. It's either π or 3.14. Except that the latter is a rational number :)
Re: Is infinity an odd or even number? (2011)
#198Earlier quoted context omitted.
I thought that most of us learn at an early age, as a result of this kind of exchange, that "infinity" is not "the biggest number" or even a number at all, as far as the ordinary notion of "number" goes.
My child mind conflated infinity and God. Or maybe I was correct, I have no idea now.
That was the adults attributing infinite and contradictory powers to their god. Church sermons will frequently mention infinity.
Re: Is infinity an odd or even number? (2011)
#199Earlier quoted context omitted.
> 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.)
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, then adding anything to it gives you {Infinity}, {Infinity {Infinity}}, etc...
Transfinite addition is not commutative!
Re: Is infinity an odd or even number? (2011)
#200[deleted]