In another thread we have the ongoing discussion of a number system [Reals] considering :

0.999... = 1 [which is currently held as a valid equation - of which the Systemic Validity is NOT in dispute]

This appears to be primarily true for this system due to the fact that it considers the following concerning the limitations in the use of infinity.

On the surface this appears to be fine.. In fact it makes a lot of sense that infinite numbers of decimal places expanding to smaller and smaller values would ultimately resolve to being smaller in magnitude to "ANY" finite number.

1] Is "being of less magnitude to any finite number" actually equal to zero?

2] Is it an "effective" or pseudo zero, borne of mathematical or systemic convenience?

3] At what point would "finite" become non-finite and how could this be determined?

Also possibly worth discussing is that:

0.999.... is actually referencing the whole number 1 as a primary source of value, which in turn is referencing zero as a way of gaining value.

after all is not 0.999.... stating a condition of 1?

How does the fact that 0.999... as being a condition of the number 1 effect the reality of 0.999... = 1?

Example: 1 - 0.999... = 1

Needless to say there are many ways of looking at this issue and I am sure you guys/gals can think of a few more...

I am of the opinion that this a more a discussion about the philosophy that underpins mathematical formulations and forms than mathematics directly.

Care to discuss?

0.999... = 1 [which is currently held as a valid equation - of which the Systemic Validity is NOT in dispute]

This appears to be primarily true for this system due to the fact that it considers the following concerning the limitations in the use of infinity.

"As the number of digits used increases without bound, the difference between 1 and the repeating decimal expansion 0.999... shrinks to be smaller in magnitude than any finite number, thus the magnitude of the difference in the limit of an infinite number of steps must be zero."

On the surface this appears to be fine.. In fact it makes a lot of sense that infinite numbers of decimal places expanding to smaller and smaller values would ultimately resolve to being smaller in magnitude to "ANY" finite number.

1] Is "being of less magnitude to any finite number" actually equal to zero?

2] Is it an "effective" or pseudo zero, borne of mathematical or systemic convenience?

3] At what point would "finite" become non-finite and how could this be determined?

Also possibly worth discussing is that:

0.999.... is actually referencing the whole number 1 as a primary source of value, which in turn is referencing zero as a way of gaining value.

after all is not 0.999.... stating a condition of 1?

How does the fact that 0.999... as being a condition of the number 1 effect the reality of 0.999... = 1?

Example: 1 - 0.999... = 1

Needless to say there are many ways of looking at this issue and I am sure you guys/gals can think of a few more...

I am of the opinion that this a more a discussion about the philosophy that underpins mathematical formulations and forms than mathematics directly.

Care to discuss?

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