Can an endless series reach its limit?

2 March, 2016 at 09:30 | Posted in Statistics & Econometrics | 2 Comments

 

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  1. There is a very simple way to determine this based on Logic 101.

    One is used to denote logical necessity aka tautology and zero, logical impossibility aka contradiction.

    This is the basis for consistency in math

    One negative result is enough to disconfirm an general proposition about an indeterminate set.

    How many positive experiments does it take to make a general proposition about an indeterminate set logically necessary?

    This is the difference between syntactical and semantic truth, and why science is said to be tentative.

  2. If you assume that 0.999.. is not equal to 1 then there must be a number X bigger than 0.999.. and less than 1. This X is impossible to find or write when using a normal method of writing 10 digit numbers (including infinite series), hence 0.999.. is identical to 1, 0.999.. can therefore be interpreted as an alternative way to write 1

    I don’t know what point you are trying to make but it seems to me your discussion of 0.999.. = 1 is missing a few points and facts.


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