All the proofs in favour of the equality 0.999... = 1 are debunked in the following article:
<snip!>
Allow me to debunk the most common fallacious proofs:
1. 1/3 = 0.333....
Well, a little known fact is that 1/3 is NOT equal to 0.333...
See Pages 33-36 of article.
2. There is no number between 0.999... and 1.
True. This is due to the fact that 0.999... is not a well-defined number.
Article explains more.
3. x = 1(0.999...)
10x= 10 (0.999...)
9x = 9(0.999...)
x = 0.999...
Wha?! Yes. If you don't do anything stupid, like try to multiply a quasi-number object by 10, you can predict the output of the algorithm exactly.
Arithmetic is designed to work with well-defined mathematical objects called the rational numbers.
For more on this, see pages 12-18.
To learn much more, read the entire article. Do visit my New Calculus site for the first rigorous formulation of calculus in history!
<snip!>
Allow me to debunk the most common fallacious proofs:
1. 1/3 = 0.333....
Well, a little known fact is that 1/3 is NOT equal to 0.333...
See Pages 33-36 of article.
2. There is no number between 0.999... and 1.
True. This is due to the fact that 0.999... is not a well-defined number.
Article explains more.
3. x = 1(0.999...)
10x= 10 (0.999...)
9x = 9(0.999...)
x = 0.999...
Wha?! Yes. If you don't do anything stupid, like try to multiply a quasi-number object by 10, you can predict the output of the algorithm exactly.
Arithmetic is designed to work with well-defined mathematical objects called the rational numbers.
For more on this, see pages 12-18.
To learn much more, read the entire article. Do visit my New Calculus site for the first rigorous formulation of calculus in history!