(*)->1

[Jean Louis <bugs@gnu.support>]

* Emanuel Berg <incal@dataswamp.org> [2023-01-13 03:23]:
> Jean Louis wrote:
> 
> >> (+) ; 0
> >
> > Why? It is wrong.
> >
> >> (*) ; 1
> >
> > Why? It is wrong.
> 
> It makes sense in the way that 0 and 1 are the identity
> elements for addition and multiplication, respectively.

I can think of it this way:nn

+ is function and it follows by nothing which is in this case
represented as zero. Nothing is zero, so result is zero. But nothing
is not zero that I know, mathematically. Zero at least has some value,
while nothing has no value.

See here:

(list) ➜ nil
(list 0) ➜ (0)

Thus (+) ➜ 0 without value result should not be zero. If no values
where given to addition, no addition has taken place. Value of zero
should not get out of nothing.

Multiplication is repeated addition.

Repeated addition of zero can't be 1.

(* 2 3) is equal (+ 3 3) ➜ 6
(* 4 3) is equal (+ 3 3 3 3) ➜ 12

How can then (*) ➜ 1 be equal to (+) ➜ 0 no matter how many times you
repeat it?

Thus this is wrong:

(+ (+) (+) (+) (+) (+) (+) (+) (+)) ➜ 0

One thing we learn here, we can finally express mathematical notation
very clearly:

for example that 2 + 2 = 4 is expressed as following from now on:

(+(+(*)(*))(+(*)(*))) ➜ 4

We can also easily teach children multiplication table every
Christmas:

(*(+(*))(+(*)(*))) ➜ 2
(*(+(*))(+(*)(*)(*))) ➜ 3
(*(+(*))(+(*)(*)(*)(*))) ➜ 4
(*(+(*))(+(*)(*)(*)(*)(*))) ➜ 5
(*(+(*))(+(*)(*)(*)(*)(*)(*))) ➜ 6
(*(+(*))(+(*)(*)(*)(*)(*)(*)(*))) ➜ 7
(*(+(*))(+(*)(*)(*)(*)(*)(*)(*)(*))) ➜ 8
(*(+(*))(+(*)(*)(*)(*)(*)(*)(*)(*)(*))) ➜ 9
(*(+(*))(+(*)(*)(*)(*)(*)(*)(*)(*)(*)(*))) ➜ 10
(*(+(*)(*))(+(*))) ➜ 2
(*(+(*)(*))(+(*)(*))) ➜ 4
(*(+(*)(*))(+(*)(*)(*))) ➜ 6
(*(+(*)(*))(+(*)(*)(*)(*))) ➜ 8
(*(+(*)(*))(+(*)(*)(*)(*)(*))) ➜ 10
(*(+(*)(*))(+(*)(*)(*)(*)(*)(*))) ➜ 12
(*(+(*)(*))(+(*)(*)(*)(*)(*)(*)(*))) ➜ 14
(*(+(*)(*))(+(*)(*)(*)(*)(*)(*)(*)(*))) ➜ 16
(*(+(*)(*))(+(*)(*)(*)(*)(*)(*)(*)(*)(*))) ➜ 18
(*(+(*)(*))(+(*)(*)(*)(*)(*)(*)(*)(*)(*)(*))) ➜ 20
(*(+(*)(*)(*))(+(*))) ➜ 3
(*(+(*)(*)(*))(+(*)(*))) ➜ 6
(*(+(*)(*)(*))(+(*)(*)(*))) ➜ 9
(*(+(*)(*)(*))(+(*)(*)(*)(*))) ➜ 12
(*(+(*)(*)(*))(+(*)(*)(*)(*)(*))) ➜ 15
(*(+(*)(*)(*))(+(*)(*)(*)(*)(*)(*))) ➜ 18
(*(+(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*))) ➜ 21
(*(+(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*)(*))) ➜ 24
(*(+(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*)(*)(*))) ➜ 27
(*(+(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*)(*)(*)(*))) ➜ 30
(*(+(*)(*)(*)(*))(+(*))) ➜ 4
(*(+(*)(*)(*)(*))(+(*)(*))) ➜ 8
(*(+(*)(*)(*)(*))(+(*)(*)(*))) ➜ 12
(*(+(*)(*)(*)(*))(+(*)(*)(*)(*))) ➜ 16
(*(+(*)(*)(*)(*))(+(*)(*)(*)(*)(*))) ➜ 20
(*(+(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*))) ➜ 24
(*(+(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*))) ➜ 28
(*(+(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*)(*))) ➜ 32
(*(+(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*)(*)(*))) ➜ 36
(*(+(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*)(*)(*)(*))) ➜ 40
(*(+(*)(*)(*)(*)(*))(+(*))) ➜ 5
(*(+(*)(*)(*)(*)(*))(+(*)(*))) ➜ 10
(*(+(*)(*)(*)(*)(*))(+(*)(*)(*))) ➜ 15
(*(+(*)(*)(*)(*)(*))(+(*)(*)(*)(*))) ➜ 20
(*(+(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*))) ➜ 25
(*(+(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*))) ➜ 30
(*(+(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*))) ➜ 35
(*(+(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*)(*))) ➜ 40
(*(+(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*)(*)(*))) ➜ 45
(*(+(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*)(*)(*)(*))) ➜ 50
(*(+(*)(*)(*)(*)(*)(*))(+(*))) ➜ 6
(*(+(*)(*)(*)(*)(*)(*))(+(*)(*))) ➜ 12
(*(+(*)(*)(*)(*)(*)(*))(+(*)(*)(*))) ➜ 18
(*(+(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*))) ➜ 24
(*(+(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*))) ➜ 30
(*(+(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*))) ➜ 36
(*(+(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*))) ➜ 42
(*(+(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*)(*))) ➜ 48
(*(+(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*)(*)(*))) ➜ 54
(*(+(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*)(*)(*)(*))) ➜ 60
(*(+(*)(*)(*)(*)(*)(*)(*))(+(*))) ➜ 7
(*(+(*)(*)(*)(*)(*)(*)(*))(+(*)(*))) ➜ 14
(*(+(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*))) ➜ 21
(*(+(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*))) ➜ 28
(*(+(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*))) ➜ 35
(*(+(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*))) ➜ 42
(*(+(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*))) ➜ 49
(*(+(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*)(*))) ➜ 56
(*(+(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*)(*)(*))) ➜ 63
(*(+(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*)(*)(*)(*))) ➜ 70
(*(+(*)(*)(*)(*)(*)(*)(*)(*))(+(*))) ➜ 8
(*(+(*)(*)(*)(*)(*)(*)(*)(*))(+(*)(*))) ➜ 16
(*(+(*)(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*))) ➜ 24
(*(+(*)(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*))) ➜ 32
(*(+(*)(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*))) ➜ 40
(*(+(*)(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*))) ➜ 48
(*(+(*)(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*))) ➜ 56
(*(+(*)(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*)(*))) ➜ 64
(*(+(*)(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*)(*)(*))) ➜ 72
(*(+(*)(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*)(*)(*)(*))) ➜ 80
(*(+(*)(*)(*)(*)(*)(*)(*)(*)(*))(+(*))) ➜ 9
(*(+(*)(*)(*)(*)(*)(*)(*)(*)(*))(+(*)(*))) ➜ 18
(*(+(*)(*)(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*))) ➜ 27
(*(+(*)(*)(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*))) ➜ 36
(*(+(*)(*)(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*))) ➜ 45
(*(+(*)(*)(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*))) ➜ 54
(*(+(*)(*)(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*))) ➜ 63
(*(+(*)(*)(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*)(*))) ➜ 72
(*(+(*)(*)(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*)(*)(*))) ➜ 81
(*(+(*)(*)(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*)(*)(*)(*))) ➜ 90
(*(+(*)(*)(*)(*)(*)(*)(*)(*)(*)(*))(+(*))) ➜ 10
(*(+(*)(*)(*)(*)(*)(*)(*)(*)(*)(*))(+(*)(*))) ➜ 20
(*(+(*)(*)(*)(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*))) ➜ 30
(*(+(*)(*)(*)(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*))) ➜ 40
(*(+(*)(*)(*)(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*))) ➜ 50
(*(+(*)(*)(*)(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*))) ➜ 60
(*(+(*)(*)(*)(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*))) ➜ 70
(*(+(*)(*)(*)(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*)(*))) ➜ 80
(*(+(*)(*)(*)(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*)(*)(*))) ➜ 90
(*(+(*)(*)(*)(*)(*)(*)(*)(*)(*)(*))(+(*)(*)(*)(*)(*)(*)(*)(*)(*)(*))) ➜ 100

-- 
Jean

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