#386 What does analysis tell us as to sqrt2 = 1.414....9994L ; new book 2nd edition: New True Mathematics



plutonium.archime...@xxxxxxxxx wrote:
(snipped)

Is sqrt2 that of two-infinite-substrings where we have 414.....
infinite substring that yields the pattern
999999 and that we have a backview infinite substring such as 99994L
where the L is a 6 carryover?

Alright, let me take analysis to the utmost and see how far I get.

The sqrt2 cannot be a infinite string of 0s because there is no way
of capturing the "2" digit out of a "1" digit, ie, the 1 in 1.414....
cannot
be a "2" unless the string ends up as this 1.9999....999L where the L
gives the needed 1 carryover to boost it to becoming 2.000...000

So we immediately rule out 0s in the 1.414...... as ending up with
2.0000.... So that leaves us with only 9s to work.

So we ask the vital question is 9 the only 9s number to have a square
root that is not fractional? Obviously 99 is fractional, so is 999,
and 9999.

I believe 9 is not the solo 9s number to be nonfractional. Somewhere
out there
is a 9s number that (like 9 itself) is nonfractional. The the square
root of 9
is nonfractional and somewhere out there is another 9s number such as
say
99999999999999999999999999999999999 ?? which is also having a square
root that is nonfractional. It may have a square root that looks like
this 414 for
its leading digits or it may look like this 732 with its leading
digits.

Now the point is, that there are an infinitude of 9s numbers that have
square roots
that are nonfractional.

Thus, we can say that an irrational number such as sqrt2 or sqrt3 or
sqrt5 or
sqrt7 are all composed of TWO substrings for which the BackView
substring
is .....9999999L and which the FrontView substring can be either
finite in length
or be infinite in length and be a mixed up kettle of digits such as
1.414....9999L

Now some would be puzzled with that BackView of 9999s

And examine the square root of 9999 of four nines which is 99.99 and
is fractional
obviously, but the point is this, there exists an infinite 9s string
for which the
square root thereof is another infinite substring of 9s

So, now the picture becomes a bit clearer as to how we can have a
square
root of 2 and end up with 1.9999....99999L and where the
multiplication of L x
L releases the 1 carryover and thus the squaring results in
2.0000...00000

And this leaves us with two tantalizing questions. Can an irrational
number like
sqrt2 be built out of two substrings, one of which is a finite
substring and the
other infinite, and the second question if the first is affirmative,
means that
the definition of Irrational as "nonrepeating blocks" is obviously
false because
the BackView is the repeating block of 9s.

This is why I say I must get out of this River of messy definitions
and correct the
definitions first.

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

Relevant Pages

  • Re: two questions on infinite substrings of decimal strings....
    ... since this substring must start at a finite ... say this when we look at the infinite string "123456...". ... Now take any one of these subsequences, which starts with digit '1' as ...
    (sci.math)
  • Re: Proof there exists a soul
    ... Robert J. Kolker wrote: ... >> therefore the exact value of the square root of two cannot exist in it. ... >> thing as the exact square root of two, since there is no infinite mind ...
    (talk.origins)
  • Newbie question(s)...
    ... next digit from previous digits... ... there are an infinite number of prime numbers ... ... I *think* that the square root of any prime number is irrational ... This is symmetric encryption, right? ...
    (sci.crypt)
  • Re: QT9xxxx A J KJxx hand again
    ... by a factor of the square root of 5 ... 6.4% .You can be 95% confident an infinitely large simulation would ... Student's "t" distribution (it will be larger the smaller the sample ... In actual fact, the number required for a full sample is far from infinite, since the number of ways the four hands can be distributed is less than 5.4 time 10 to the 28th power and my calculator says the way that the other hands can be distributed once you know one hand looks to be about 8.3 times 10 to the 16th..... ...
    (rec.games.bridge)
  • Re: two questions on infinite substrings of decimal strings....
    ... since this substring must start at a finite ... Is this reasoning correct? ... No - the "tail" of the decimal string starting at any finite position still ... all infinite decimal expansions as substrings - ...
    (sci.math)
Quantcast