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Yes, it definately does. There are other ways to prove it, also.
EDIT: Reffering to 0.99... = 1, of course.
[edited by - cowsarenotevil on August 30, 2003 7:54:00 PM]
EDIT: Reffering to 0.99... = 1, of course.
[edited by - cowsarenotevil on August 30, 2003 7:54:00 PM]
quote:
Original post by Crispy
188 = 1
WTF? Proofs I say! I want proofs!
quote:
Original post by GarlandIX
I disagree. 0.999999999999.... is 0.00000000000...1 less than 1.
Please explain to me how that 1 at the end would ever be reached?
quote:
Original post by cowsarenotevilquote:
Original post by GarlandIX
I disagree. 0.999999999999.... is 0.00000000000...1 less than 1.
Please explain to me how that 1 at the end would ever be reached?
It can''t. Welcome to infinity, or as I like to call it "1/0".
"A socialist is a communist who didn''t try hard enough."
- Me
quote:
Original post by cowsarenotevilquote:
Original post by Crispy
188 = 1
WTF? Proofs I say! I want proofs!
Dammit, man - are you a man or a cow. Oh wait - cow is in your name, but I just called you a man. Holy pretzels, I''ve gone crosseyed...
Anyway, here''s the proof you seek:
STEP 1: physically enlarge and pixelate left hand side of the equasion:
100
100
STEP 2: add imaginary line to the left hand side of the equation
100
---
100
STEP 3: evaluate the left hand side of the equation
100
--- = 100 / 100 = 1.0
100
STEP 4: compare the left hand side of the equation to the opposing right hand side of the same equation
1 = 1
Q.E.D.
Actually this works best if written by hand on paper - what you witnessed above is he effect of digital degeneration
Quoting the book Real Analysis 3rd ed. by H.L.Royden
Page 40, #22:
For those of you who don''t get what I just quotes, the sequence an is the decimal expansion of a number when p=10 (base 10) and when a number is of the form q/pn (i.e. a "special" rational number whose denominator is a factor of some power of 10) then there exists two such expansions in decimal form for the number, one being the finite representation of the number, and the other being an infinite series summing up to that number.
In this case, 1 is 1/1 = 1/(10^0) is of this special form, and thus there exists two decimal representations for the number, namely 1 and 0.999999....
Page 40, #22:
quote:
Let p be an integer greater than 1, and x a real number, 0 < x < 1.
There exists a sequence <an> of integers with 0 <= an < p such that x = Sum n:1->inf (an / pn) and this sequence is unique except when x is of the form q/pn, in which case there are exactly two such sequences.
For those of you who don''t get what I just quotes, the sequence an is the decimal expansion of a number when p=10 (base 10) and when a number is of the form q/pn (i.e. a "special" rational number whose denominator is a factor of some power of 10) then there exists two such expansions in decimal form for the number, one being the finite representation of the number, and the other being an infinite series summing up to that number.
In this case, 1 is 1/1 = 1/(10^0) is of this special form, and thus there exists two decimal representations for the number, namely 1 and 0.999999....
quote:
Original post by AnonymousPosterChild
It can''t. Welcome to infinity, or as I like to call it "1/0".
Can it really be proved that 1/0 is infinity? I thought not.
quote:
Original post by Cedric
Not just there... *Sigh*
I was wondering if anybody else remembered the 4 (or was it more?) paged fight between believers and non-believers here...
Colin Jeanne | Invader''s Realm
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