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Is it Tommy somewhere
#1
Hi, Tetration Community

is it active a user called Tommy, if it is the case then :

w = (-3 # +5 # *11 # @23)
reciprocalOf(w) = -(5068/228144) # +(5572/228144) # *(364/228144) # @16156/228144)
w·reciprocalOf(w) = -1 # +1 @ *1 # @2 = @1
path :
w = -a # +b # *c # @d
where # is addition symbol in p4
example with -3 # +5 # *11 # @23
1/w = 1/(-a # +b # *c # @d)
w~= -'a # +b # *'c # @d
where s' m <-> aditiveInverseOf( sm )
1/w = (1/w)(w~/w~) = w~/(ww~)
w~/(ww~) = (-'a # +b # *'c # @d ) / ( ( -a # +b # *c # @d) (-'a # +b # *'c # @d) )
w~/(ww~) = (-'3 # +5 # *'11 # @23) / ( ( -3 # +5 # *11 # @23)(-'3 # +5 # *'11 # @23) )
w~/(ww~) = (-'a # +b # *'c # @d ) / (+'a^2 # @b^2 # +'c^2 # @d^2 # @'2ac # +2bd )
w~/(ww~) = (-'3 # +5 # *'11 # @23) / ( +'9 # @25 # +'121 # @529 # @'66 # +230 )
Note that is enough with express the statement just with the signs @, + ,@' and +'
and is not necessary convert if remain symbol @' and +'...
w~/(ww~) = (-'3 # +5 # *'11 # @23) / ( @480 # +100 )
Now, we complete to make difference of squares in the denominator , but
one must be careful to complete it towards the greatest number, not the smallest
as (x # y)(x # y') if x>y, or as (x # y)(x' # y) if x<y
..in this case we keep @480 invariable in the difference of squares, since it s the greatest
(w~z)/(ww~z) = ( (-'3 # +5 # *'11 # @23)(@480 # +'100) ) / ( (@480 # +100)(@480 #
+'100) )
(w~z)/(ww~z) = ( (-'3 # +5 # *'11 # @23)(@480 # +'100) ) / ( @228144 )
(w~z)/(ww~z)=(-'1464 # +2440 #*'5368 # @11224 #*300 #@'500 # -1100
#+'2300)/@228144

(w~z)/(ww~z) = ( -5068 # +5572 # *364 # @16156 )/@228144
hammering the neutral-signed terms upwards
(w~z)/(ww~z) = -(5068/228144) # +(5572/228144) # *(364/228144) # @16156/228144)
(w~z)/(ww~z) = reciprocalOf( w )

https://groups.google.com/g/sci.math/c/m...IMz54hBwAJ

Best regards Grasshoppa Wink
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#2
I assume you are asking if Tommy is a member here? He is. But I don't think anyone here will know what any of this means, besides Tommy.
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#3
(08/17/2021, 03:23 AM)JmsNxn Wrote: I assume you are asking if Tommy is a member here? He is. But I don't think anyone here will know what any of this means, besides Tommy.

the poster is talking about some higher dimensional numbers.

Hi " grasshopper " Smile

Yes it is indeed me. 
The same tommy1729 Smile

welcome.

That being said , this forum is mainly about tetration and complex numbers.
You already have me on social media.
The level of math here is typically above sci.math , especially since 2021.

Some people might remember me from being " critical " about ZFC.

regards

tommy1729
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#4
Well, although Tim would write something like

(- 3 + 5 * 11 # 23)( - (5068/228144) + (5572/228144) * (364/228144) # (16156/228144) ) = #1


I just google a bit, and stumble upon one of your webs, but I was in doubt if you were the same Tommy1729 as in
the newsletter Smile

""The level of math here is typically above sci.math , especially since 2021.""

It is a bit messy the newsletter, jeje

""That being said , this forum is mainly about tetration and complex numbers.""

:V


cheers, grassshopper

https://archive.org/details/polysignedpacmanproduct
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#5
(08/19/2021, 11:24 PM)grassshopper Wrote: Well, although Tim would write something like

(- 3 + 5 * 11 # 23)( - (5068/228144) + (5572/228144) * (364/228144) # (16156/228144) ) = #1


I just google a bit, and stumble upon one of your webs, but I was in doubt if you were the same Tommy1729 as in
the newsletter Smile

""The level of math here is typically above sci.math , especially since 2021.""

It is a bit messy the newsletter, jeje

""That being said , this forum is mainly about tetration and complex numbers.""

:V


cheers, grassshopper

https://archive.org/details/polysignedpacmanproduct

Thanks for the reply.

the pacman product or numbers seem to loose alot of usual properties.

so i wonder if you have special motives to consider this algebra.

you might want to look at the thread " tommy quaterion " where I posted 3 types of commutative 4D numbers and an 8D commutative number system :

https://math.eretrandre.org/tetrationfor...p?tid=1288

regards

tommy1729
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