## Baby Sister Numbers |
November 3rd, 2021 |

kids, math |

The largest number is

.*Noranoo*If you try and make any larger number, you still get

. For example,*Noranoo*

, and*Noranoo*+ 1 =*Noranoo*

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

, dubbed "*Noranoo*- 1

". This means*Norklet*

, while*Noranoo*- 1 + 1 =*Noranoo*

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

is*Noranoo** -1

. It is the smallest number, and like*Norahats*

any attempt to go lower keeps you at*Noranoo*

.*Norahats*These 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 be *Norahats* * -1 * -1 * -1

and not
*Norklet*

, but Lily insisted that
*Noranoo*

and *Noranoo*

were
equal in magnitude.
*Norahats*

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