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Topic: Why is there a difference between fractions 1/3 and .333
repeating multiplied by 3

Replies: 4   Last Post: Oct 2, 2017 6:09 PM

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Dan Christensen

Posts: 8,219
Registered: 7/9/08
Re: Why is there a difference between fractions 1/3 and .333
repeating multiplied by 3

Posted: Oct 2, 2017 1:09 PM
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On Monday, October 2, 2017 at 11:54:59 AM UTC-4, John Gabriel wrote:

> To discuss difference between 0.999... and 1 or 0.333... and 1/3 is like trying to discuss the difference between apple and football. They are different objects.

Wrong again, Troll Boy.

0.999... = 0.9 + 0.09 + 0.009 + ... = 1

Similarly, 0.333... = 0.3 + 0.03 + 0.003 + ... = 1/3

Only trolls like you question this.

> Euler in a moment of grand folly decided to define these as equal, that is, S = Lim S where S = 0.333... or S = 0.999...

Wrong again, Troll Boy. Repeat your lies as often as you like, but as you yourself were recently forced to concede when confronted with the evidence, "Of course he [Euler] did not write 'Lim S'... He did not talk about S." (May 27, 2017)

> The limit in both cases is a well-formed number.
> The limit of the series represented by 0.333... is 1/3.

So, they are equal.

> Euler's Blunder is about defining the series 0.333... = 1/3.

Nothing wrong with that, Troll Boy. They are interchangeable. No wonder you failed math.


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