0.9999999… = 1 (exactly, not approximately). This is easily provable.

Thus, -0.9999999… = -1,
√(0.9999999…) = √(1) = 1, and
+0.9999999… = +1 = 1.

I don't understand why it would be necessary to have a new way of looking at it.

GeniusIsBack wrote:

Before any Confusion!?  ( The Root ) is Not The Square Root...

GiB.

Any confusion is due solely to the unnecessary new terminology, not due to the fact that 0.999999… is exactly equal to 1.

Please define the terminology you are using.

Quote: ALL_Is_Number (Strange Name!) "Any confusion is due solely to the unnecessary new terminology, not due to the fact that 0.999999… is exactly equal to 1. Please define the terminology you are using. "

GiB. The Terminology is Quite simple!...

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Root

To turn up or to dig out with the snout; as, the swine roots
the earth.

Root Root, n. [Icel. r[=o]t (for vr[=o]t); akin to E. wort,
and perhaps to root to turn up the earth. See Wort.]
1. (Bot.)
(a) The underground portion of a plant, whether a true
root or a tuber, a bulb or rootstock, as in the
potato, the onion, or the sweet flag.
(b) The descending, and commonly branching, axis of a
plant, increasing in length by growth at its extremity
only, not divided into joints, leafless and without
buds, and having for its offices to fix the plant in
the earth, to supply it with moisture and soluble
matters, and sometimes to serve as a reservoir of
nutriment for future growth. A true root, however, may
never reach the ground, but may be attached to a wall,
etc., as in the ivy, or may hang loosely in the air,
as in some epiphytic orchids.

2. An edible or esculent root, especially of such plants as
produce a single root, as the beet, carrot, etc.; as, the
root crop.


3. That which resembles a root in position or function, esp.
as a source of nourishment or support; that from which
anything proceeds as if by growth or development; as, the
root of a tooth, a nail, a cancer, and the like.
Specifically:
(a) An ancestor or progenitor; and hence, an early race; a
stem.


They were the roots out of which sprang two
distinct people. --Locke.

(b) A primitive form of speech; one of the earliest terms
employed in language; a word from which other words
are formed; a radix, or radical.
(c) The cause or occasion by which anything is brought
about; the source. "She herself . . . is root of
bounty." --Chaucer.


The love of money is a root of all kinds of
evil. --1 Tim. vi.
10 (rev. Ver.)

(d) (Math.) That factor of a quantity which when
multiplied into itself will produce that quantity;
thus, 3 is a root of 9, because 3 multiplied into
itself produces 9; 3 is the cube root of 27.
(e) (Mus.) The fundamental tone of any chord; the tone
from whose harmonics, or overtones, a chord is
composed. --Busby.

(f) The lowest place, position, or part. "Deep to the
roots of hell." --Milton. "The roots of the
mountains." --Southey.

4. (Astrol.) The time which to reckon in making calculations.

When a root is of a birth yknowe [known]. --Chaucer.


Aerial roots. (a) Small roots emitted from the stem of a plant in the
open air, which, attaching themselves to the bark of
trees, etc., serve to support the plant.
(b) Large roots growing from the stem, etc., which descend
and establish themselves in the soil. See Illust. of
Mangrove.

Multiple primary root a name given to the numerous
roots emitted from the radicle in many plants, as the
squash.

Primary root the central, first-formed, main root,
from which the rootlets are given off.

Root and branch, part; wholly; completely; as, to
destroy an error root and branch.

Root-and-branch men, reformers; -- a designation
applied to the English Independents (1641). See Citation
under Radical, n., 2.

Root barnacle one of the Rhizocephala.

Root hair one of the slender, hairlike fibers found
on the surface of fresh roots. They are prolongations of
the superficial cells of the root into minute tubes.
--Gray.

Root leaf a radical leaf. See Radical, a., 3
(b) .

Root louse any plant louse, or aphid, which lives
on the roots of plants, as the Phylloxera of the
grapevine. See Phylloxera.

Root of an equation that value which, substituted
for the unknown quantity in an equation, satisfies the
equation.

Root of a nail
(Anat.), the part of a nail which is covered by the skin.


Root of a tooth the part of a tooth contained in
the socket and consisting of one or more fangs.

Secondary roots roots emitted from any part of the
plant above the radicle.

To strike root, take root}, to send forth roots; to
become fixed in the earth, etc., by a root; hence, in
general, to become planted, fixed, or established; to
increase and spread; as, an opinion takes root. "The
bended twigs take root." --Milton.

   
Root Root, v. i. [AS. wr[=o]tan; akin to wr[=o]t a snout,
trunk, D. wroeten to root, G. r["u]ssel snout, trunk,
proboscis, Icel. r[=o]ta to root, and perhaps to L. rodere to
gnaw (E. rodent) or to E. root, n.]
1. To turn up the earth with the snout, as swine.


2. Hence, to seek for favor or advancement by low arts or
groveling servility; to fawn servilely.


   
Root Root (r[=oo]t), v. i. [imp. & p. p. Rooted; p. pr. &
vb. n. Rooting.]
1. To fix the root; to enter the earth, as roots; to take
root and begin to grow.


In deep grounds the weeds root deeper. --Mortimer.


2. To be firmly fixed; to be established.


If any irregularity chanced to intervene and to
cause misappehensions, he gave them not leave to
root and fasten by concealment. --Bp. Fell.

Root Root, v. i. [Cf. Rout to roar.]
To shout for, or otherwise noisly applaud or encourage, a
contestant, as in sports; hence, to wish earnestly for the
success of some one or the happening of some event, with the
superstitious notion that this action may have efficacy; --
usually with for; as, the crowd rooted for the home team.
[Slang or Cant, U. S.]


   
Root Root, v. t.
1. To plant and fix deeply in the earth, or as in the earth;
to implant firmly; hence, to make deep or radical; to
establish; -- used chiefly in the participle; as, rooted
trees or forests; rooted dislike.


2. To tear up by the root; to eradicate; to extirpate; --
with up, out, or away. "I will go root away the noisome
weeds." --Shak.


The Lord rooted them out of their land . . . and
cast them into another land. --Deut. xxix.
28.

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GiB.

Now that is Clear to you!? But we are of course talking about a Math Root Maybe you Mean The square root, the cube root, or more generally the nth root of a number. ... A root system of vectors, whose elements are called roots. ...

This is where Good old Common Sense comes in! ( THE ROOT IS THE START! THE ORIGIN! ) as in the Example 100.

Hi ARB,

Let x = 0.999...

10x = 9.999...

9x = 9

x = 1

But wait! We let x = 0.999...

Therefore 0.999... = 1.

What is the problem with this proof? Which line contains the error?

Also weren't you banned before? (for trolling or insulting or something, i read the old thread)

Hi dolgopolov;

Welcome to the forum. How do you know that?

Okay. I understand perfectly. Please do not let it upset you, try to enjoy the forum anyway.

So Now all we have to find is...


Infinite-Recurring 0.9 Negative = ?

Infinite-Recurring 0.9 Root = ?

Infinite-Recurring 0.9 Positive = ?


A Better way of Looking at the above is   IR0.9N( ? )  IR0.9R( ? )  IR0.9P( ? )



It Helps!...if Everyone stays Focused on the Problem! Now ( ROOT ) is Fully Understood.


GiB.

hi, can you explain what you mean?

we have proven that 0.999... = 1

you also want us to prove -0.999... = -1?

let x = -0.999...

10x = -9.999...

9x = -9

x = -1

so now -0.999... = -1

what do you mean by root? square root?

well i have just proven that 0.999... = 1 so if both are the same then square root of both should surely be the same?

also what is "IR0.9N( ? )  IR0.9R( ? )  IR0.9P( ? )"

Just For ALL_Is_Number


100 Root = 100  ( THE ROOT IS THE START! THE ORIGIN! ) (The Root) is Not The Square Root) And Just In case Anyone Thinks It's Teeth? Etc.


GiB.

100 Root = 100?

by root you mean...the origin? ok, what does this have to do with the original problem?

you are telling us something about 0.999... and something about understanding the root but you are being very vague still

Hi guys;

It is not going to pay to press him any further on "what he has got." As you both know there is nothing to have here.
In the interest of presenting good math I am forced to say that argument is fruitless. There are many proofs that prove him wrong. If he will not look then he cannot see.

well, i am interested in seeing if he can provide a good argument, at least....