sci.physics

Archimedes Plutonium wrote:

>
> The way I am going to define P-adic addition, multiplication,
> subtract, divide, roots, powers
> is that I am going to stay as close as possible to Reals operations of
> the same.
>
> For example adding ..........999999 with ......9999999 would be this
>
> .....99999999.
> +...99999999.
> ---------------------
>
> And defined by Reals as a sequence of additions as such
>
> 9
> +9
> -----
> 18
>
> 99
> +99
> -------
> 198
>
> 999
> +999
> -------
> 1998
>
> And so, from Reals, we have the P-adic of 10-adics addition of .....
> 99999 and .....9999
> as that of .......999999998
>
> In a similar manner I define the operation of exponentiation for p-
> adics by using the Reals
> in sequence form


Where to get the answer as to what is 3^.......333333333

>
> 3^3
>
> then
>
> 3^33
>
> then
>
> 3^333
>

Someone wrote:


>
> 3^3 = 27
> 3^33 = 5559060566555523
> 3^333 =
> 7609880231320598097204258672650327807278963563720778651170100370357916\
>
> 31439306199613044145649378522557935351570949952010001833769302566531786879537\
> 190794573523
> 3^3333 =
> 175849841268201098336769354533279819155535543744632506688392137212205\
>
> 31529760308103321403089710700075959461629724493241033779589043022231485974662\
>
> 95048772268773918500088273490159180926995708653866784723455399203770399357905\
>
> 53656365318400798719582380133795913694293219427166987880470337131012388418624\
>
> 83338885707867606741513058036291112738587093933051138048758992922812937939203\
>
> 93770248428093368059565557597910526627445129778483904756486102163600659097389\
>
> 03668369030280641024027466127285984774874066682918935158339962055582236833605\
>
> 24455397511667353832120385799678766096079941796319000924535589083647722940083\
>
> 44595075671498385681157912821796447292113208801397598687104433346731424780904\
>
> 75307943510853933125046529467820827257161691269300659439016758445605750048527\
>
> 44043597646635161110283870331083777996697226955533929226406687958894504840216\
>
> 12150297990169709691787425101795614051705479128270044197034769726418157375120\
>
> 43597739782517010962009394978209273534165277226966096926963912592672868354616\
>
> 53664233773329811882745513459769315322073196394683769737461989774812742303491\
>
> 73276584959333045342726285469128172374035380620503336188925806158976849013879\
>
> 69461176819949794013175089371634463090749837340633243486833656176432584406911\
>
> 56891541095586781101177637535890049798492832019786118527532541721223284160219\
>
> 36478929095733504199463614576372219847041891388471392798927415072136365035718\
>
> 13220921625083385956728694846049061868862402893874287897997715652990850139154\
>
> 04197052081883361722255527982545373799281613135391911470757690056688137622636\
> 76789617615308716172367747466666483286894183470273414753523

So what remains the same after the sequence from 3^3 to that of 3^3333
is the digits ..........3523

We cannot tell if the next digit is going to be a 5 or perhaps a 7 or
something else and so
we have to go out to 3^33333 and then 3^333333 and so on as we build
our answer as to
what 3^......333333333 is.

So the answer so far is that 3^......33333333 = .......3523 and if
someone needs more of an answer
they have to multiply out further to elaborate further on the answer.

In this manner, Exponentiation is defined for Infinite Integers and P-
adics.

Resuming discussion with e^(pi)(i) = (-1).

5-adic square roots of (-1)
.......

and

.....

Pi and e are Reals as such:

......

and

.......

Using (e) as 3 and (pi) as 3 to make things easier, let us do a trial
run and taking (i) as
....1323.

We have 3 x ....1323 giving us ......3969 for (pi) x (i)

Now for e^ (pi) x (i) we have 3^ ....3969

So what is

3^9

then

3^69

then

3^969

then

3^3969

Is it going to be close to .......9999? I doubt it.

So what number, call it Z such that ^Z is going to give me .....
999999999

Is it a number that is somewhere inbetween ......03030303. and .....
303030.
if I can describe "inbetween".

So what I am hunting for here is a Z number which is ^Z = ....
999999

Archimedes Plutonium
/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies