Baby Sister Numbers

5flowerfeatherfocus

6Slider

3flowerfeatherfocus

2jefftk

2Slider

2jefftk

2Slider

3ejacob

3TLW

5jefftk

2Vanessa Kosoy

3jefftk

4Vanessa Kosoy

5jefftk

3jefftk

2tailcalled

3Vanessa Kosoy

1tailcalled

2jefftk

1tailcalled

2jefftk

2Dagon

3Slider

2jefftk

2Slider

14jefftk

2Slider

35Ericf

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28 comments, sorted by Click to highlight new comments since: Today at 5:50 AM

This is great! It reminds me a bit of ordinal arithmetic, in which addition is non-commutative. The ordinal numbers begin with all infinitely many natural numbers, followed by the first infinite ordinal, . The next ordinal is , which is greater than . But is just .

Subtraction isn't canonically defined for the ordinals, so isn't a thing, but there's an extension of the ordinal numbers called the surreal numbers where it does exist. Sadly addition is defined differently on the surreals, and here it is commutative. does exist though, and as with

does equal .*Norahats*

The surreals also contain the infinitesimal number , which is greater than zero but less than any real number. it's defined as the number between on the left and all members of the infinite sequence on the right. Not exactly

(), but not too far away: :)*Norklet*

(h/t Alex_Altair, whose recent venture into this area caused me to have any information whatsoever about it in my head)

That was mainly the motivation for my counting question but the answer isconsistent with Noranoo invoking transfinite induction to get counted.

I think the pattern of -"Is it possible to count to Noranoo?" -yes and -"Can I count to Noranoo?" -no would isolate only transfinite induction.

Another way this could be asked as a dad joke is if ever one is tired and being asked about it claim that "I spent the night counting to Noranoo". If this story is incredile then it is recognised as a supertask. If there is a reaction like "wow you count fast" that would point to it being some very high finite integer.

I guess I am trying to fish for a scneario that would prompt a resonpce that would clearly support that. Another approach that would more strongly differentiate against googol-likeness would be to start counting and then increasingly blur the words together and then slow down "... norklet, noranoo" the thinking going that even if your mouth was perfectly dexterous the counting might detect "cheating detection" as it migth not be respectful of the vastness of the number.

But to be frank it was more that I thought I kinda understood the difference but I find myself struggling to figure out what would be a fair operationalization, suggesting I don't understand it.

I asked Lily, and she told me that Noranoo is even, so I guess it isn't prime. Norklet is odd, but she doesn't know what prime means so I don't have a good way to find out.

The product of all primes below Noranoo is (not asking Lily) Noranoo. (Because otherwise it would be greater than Noranoo, and so clamps to Noranoo)

The sum of all positive integers below Norklet is Noranoo, since again it clamps.

A few days ago, Lily (7y) told me about some Nora-inspired numbers:

The largest number is

.NoranooIf you try and make any larger number, you still get

. For example,Noranoo

, andNoranoo+ 1 =Noranoo

.Noranoo* 2 =NoranooOtherwise, it behaves normally. You can have

, dubbed "Noranoo- 1

". This meansNorklet

, whileNoranoo- 1 + 1 =Noranoo

. This didn't bother her.Noranoo+ 1 - 1 =Norklet

isNoranoo* -1

. It is the smallest number, and likeNorahats

any attempt to go lower keeps you atNoranoo

.NorahatsThese are very large numbers: much bigger than a googol.

This is a kind of saturation arithmetic, more of a computersy approach than a mathy one, since you give up associativity, distributivity, the successor function being an injection, and all that.

On the other hand, it's slightly more elegant than a typical computational implementation of saturation, because it is symmetric around zero. Normally, you are using some number of bits, which gives you 2^N distinct values, and so an even number of integers. Typically we set the minimum integer to be one larger, in absolute value, than the maximum one. In this case, though, there are an odd number of integers. I asked whether perhaps

could beNorahats* -1 * -1 * -1

and notNorklet

, but Lily insisted thatNoranoo

andNoranoo

were equal in magnitude.NorahatsComment via: facebook