If you add three thirds do you get a whole? I Can't.
1/3=.333333
+
1/3=.333333
+
1/3=.333333
=
1=.999999
=
?
still my favorite...
Let X = .9999...
then 10X = 9.9999....
subtract left sides and right sides of the equations
10X = 9.9999...
- X = .9999...
------------------------------
9X = 9.0000000
divide both sides by 9:
X = 1
.999 = 1
Q.E.D! -T
... = infinite.
If (A)=(B), and (C)=(D), then (C)-(A) = (D)-(B).
(A) is X, (B) is .999..., (C) is 10X, and (D) is 9.999...
So, (10X - X) = (9.999... - .999...)
9X = 9.000
X = 1
Yeah, they may call this online or in classrooms the limit of the sequence of numbers (I'm a high school drop out and saw that term first on the link). Shall we move on to vortex's where the exterior is measurable but the interior not? -T
Master Shake,
Try looking at it this way.
If (A)=(B), and (C)=(D), then (C)-(A) = (D)-(B).
(A) is X, (B) is .999..., (C) is 10X, and (D) is 9.999...
So, (10X - X) = (9.999... - .999...)
9X = 9.000
X = 1