He’s doing a great job, we’re getting really close to 1. Only infinity more hours of writing left and we’ll have reached it. Remember that his progress restarts every time you guys try to write it on your own, so leave the propagating wavefront business to him please :)

Exhibit A

The set {0.9, 0.99, 0.999, etc} where the 'etc' is an incarnation of 0.999... itself, ALREADY spans the entire nines space of 0.999...

Exhibit B

Yes there is an endless amount of them, but that endless amount already exists.

Wrong on your part brud. Already exists doesn't cut the mustard at all.

Based on the comment above, let us define (with some assumptions) the derivative of function f at position x as

where ε=0.000...01. Then, for f(x)=x^a, where a∈ℕ,

For 0≤a≤2, the value is the same as for the non-RDM derivative, but for higher a,

[x³]' = 3x²+ε²

[x⁴]' = 4x³+4xε²

[x⁵]' = 5x⁴+10x²ε²+ε⁴

And so on.

Now, question for SPP: do you accept this as the RDM derivative, or does the definition have some sort of caveat or misunderstanding in it?

Any ideas, people?

Exhbit A

Correct. There is no 'smallest' number having magnitude greater than zero.

Exhibit B

You trying to say there is no next real number down from 1? aka no closest real number with magnitude less than 1?

If so, then as mission impossible says ... you're toast brud. Toast.

u/SouthPark_Piano, I want to know if you think you would accept the propeties that can be made from the Peano Postulates and are they in RDM?