A few days ago, Lily (7y) told me about some Nora-inspired numbers:
The largest number is
If you try and make any larger number, you still get
Noranoo. For example,
Noranoo + 1 = Noranoo, and
Noranoo * 2 = Noranoo.
Otherwise, it behaves normally. You can have
Noranoo - 1, dubbed "
Norklet". This means
Noranoo - 1 + 1 = Noranoo, while
Noranoo + 1 - 1 = Norklet. This didn't bother her.
Noranoo * -1is
Norahats. It is the smallest number, and like
Noranooany attempt to go lower keeps you at
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
Norahats * -1 * -1 * -1
Norklet and not
Noranoo, but Lily insisted that
equal in magnitude.
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