On: 0.999...= 1

[gspr]

> 0.00...1

And what does this mean? I will remind you that for an integer d between 0 and 9, 0.ddd… means the limit of \sum_{i=1}^N d/10^i as N tends to infinity.

[brutt → gspr]

  0.000...1 = 1/∞

[gspr → brutt]

And what does the right hand side of that mean? Division is commonly defined for a real numerator and a real, non-zero denominator. You are using the common symbol, but with ∞ in the place of the denominator. Since ∞ is not a real number, you must be using a non-standard definition of division, and have to define what you mean.

[brutt → gspr]

In some systems, division by ∞ is not defined at all (forbidden), in other it defined as 0, in another systems it defined as non zero.

[gspr → brutt]

> In some systems, division by ∞ is not defined at all (forbidden), in other it defined as 0, in another systems it defined as non zero.

Fine by me. Define whatever notion you're using. You can't just throw out non-standard things and expect people to know what you mean.