In article <mKSdne976K37EYrVnZ2dnUVZ_vGdnZ2d@[EMAIL PROTECTED]
>,
Not=
@[EMAIL PROTECTED]
says...
> Please bear with me if I am not following a protocal for the group.
>=20
> My step daughter is in 9th grade math (she is in 7th grade).
> She asked me earlier in the week if .999 going off in to infinity is
the=
=20
> same thing as 1.
>=20
> I said no. Close...but no.
> I am by far no pro at math.
> She insists its the same, because her math teacher said so...
First thing is, the math teacher is correct. They are the same number -
eve=
n if they are written differently. Maybe the=20
best way to try to understand this is as follows:
If you have two numbers, x and y, you can tell if they are the same or
diff=
erent by subtracting one from the other. If=20
the result is zero then the numbers are the same, if it is not zero then
th=
e numbers are different. If you try to=20
subtract 0.9999999999999.... from 1.0000000000.... then you get a result
of=
0.0000000000.... Note that the zeros in the=20
result go on for ever, every digit is zero, there is not some '1' or '3'
hi=
dden somewhere after n digits. And=20
0.000000...... ,. with zeros going on for ever is just the regular zero or
=
'o' that you know and understand from the=20
maths you might still remember. So x-y (in this case) =3D 0, and x =3D y,
o=
r 1.000000..... =3D 0.99990..... .=20
If you can't understand this arguement then it is likely that your
conceptu=
al understanding of math is insufficient to=20
get a grasp of it. I'm not trying to be insulting here - after-all, it
took=
a lot of very clever mathematicians many=20
hundreds of year s to formalise mathematics sufficiently to be able to
answ=
er questions such as this.
> But, I do seem to remember a math teacher telling me that mathmatically,
=
it=20
> can be the same as one. In reality it is not. He told me to think of
tw=
o=20
> lines. To be parallel, the need to be the same distance apart...say 1.
=
If=20
> they are .999999 apart...eventually they will meet. And, no matter how
f=
ar=20
> out you go in to infinity, you still will not reach 1.
If the math teacher really said exactly that to you then he/she may not
hav=
e been a very good teacher - it seems to me=20
to be a particularly confusing arguement. Maybe another way to help you
und=
erstand is to recognise that the things we=20
write down on paper '1', '1/2', 'Sqrt(2)', 'pi', '3.14159',
'0.9999999999',=
are not actually numbers, they are just=20
symbols that represent numbers. In the same way that 'blue', written on a
p=
age is not a color, it is just a symbol that=20
represents the color of the sky, an artifact that allows us to identify
and=
describe things. If someone writes 'bleu',=20
or 'azul', it looks different on the paper, but it represents the same
conc=
ept. Likewise, "the year of Shakespeare's=20
death" and "the year of the birth of Frederick, Count Palatine of
Zweibr=FC=
cken" are both synonyms for "1616".=20
Decimal format, is a powerful way to write numbers, particularly because
it=
simplifies arithmatical procedures, such as=20
+,-,*,/,>,<, etc, compared to working in fraction. For example it is
easier=
to tell that 0.538461... is bigger than=20
0.57275727..., than it is to tell that 7/13 is bigger than 29/55. But
decim=
als do have some complicatons. For example=20
you can write 1 as '1', or '1.0', or as '1.000...' and they all represent
t=
he same thing. A fraction like 1/2 can be=20
written as '0.5' without any more digits, but 1/3 is '0.33333.....' (with
t=
he '3's going on for ever), and pi (the=20
ratio between the cir***ference and diameter of a circle is a number that
s=
tarts off '3.14159...' and goes on for ever=20
with no pattern in the ensuing digits. It just happens to be the case that
=
1 and 0.999... are synonyms for the same=20
number, even though they look different.=20
Finally, an alternate arguement that might convince you:=20
1/3 + 1/3 + 1/3 =3D 3/3 =3D 1 exactly.
1/3 =3D 0.333.......
so 1/3 + 1/3 + 1/3 =3D 0.333... + 0.333... + 0.333... =3D 0.999... =3D 1
(a=
s shown on the first line).
Best to remember that math can be counter-intuitive sometimes, but it is
ve=
ry unlikely that all those mathematicians=20
have somehow "got it wrong".
Hope this helps,
Mike
There are=20
> Best I can think of is that this is a mathmatical concept, that exists
on=
=20
> paper....
> Can anyone here give an answer that makes sense to me, or her?
> Thanks....
=20
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