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(*)->1
From: |
Jean Louis |
Subject: |
(*)->1 |
Date: |
Fri, 13 Jan 2023 09:21:53 +0300 |
User-agent: |
Mutt/2.2.9+54 (af2080d) (2022-11-21) |
* 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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- Re: algorithmic Lisp language (was: Re: How to make M-x TAB not work on (interactive) declaration?), (continued)
- Re: How to make M-x TAB not work on (interactive) declaration?, Tassilo Horn, 2023/01/08
- Re: How to make M-x TAB not work on (interactive) declaration?, Eli Zaretskii, 2023/01/08
- Re: How to make M-x TAB not work on (interactive) declaration?, Jean Louis, 2023/01/08
- RE: [External] : Re: How to make M-x TAB not work on (interactive) declaration?, Drew Adams, 2023/01/08
- Re: [External] : Re: How to make M-x TAB not work on (interactive) declaration?, Emanuel Berg, 2023/01/09
- Re: [External] : Re: How to make M-x TAB not work on (interactive) declaration?, Jean Louis, 2023/01/09
- Re: [External] : Re: How to make M-x TAB not work on (interactive) declaration?, Emanuel Berg, 2023/01/12
- (*)->1,
Jean Louis <=
- Re: (*)->1, Michael Heerdegen, 2023/01/14
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- Re: [External] : Re: How to make M-x TAB not work on (interactive) declaration?, Rudolf Adamkovič, 2023/01/15
- Re: [External] : Re: How to make M-x TAB not work on (interactive) declaration?, Jean Louis, 2023/01/15
- RE: [External] : Re: How to make M-x TAB not work on (interactive) declaration?, Drew Adams, 2023/01/15
- Re: [External] : Re: How to make M-x TAB not work on (interactive) declaration?, Jean Louis, 2023/01/16
- RE: [External] : Re: How to make M-x TAB not work on (interactive) declaration?, Drew Adams, 2023/01/16
- Re: [External] : Re: How to make M-x TAB not work on (interactive) declaration?, Jean Louis, 2023/01/16
- RE: [External] : Re: How to make M-x TAB not work on (interactive) declaration?, Drew Adams, 2023/01/16
- Re: [External] : Re: How to make M-x TAB not work on (interactive) declaration?, tomas, 2023/01/17