Dear friend, you are wrong. If you look at the original paper (the main uniqueness theorem), then you find that the condition "nondecreasing or nonincreasing" is correct and is clearly different to the hypothesis " UXP' is a constant".
andydude Wrote:I feel like I have come to a resolution to this issue on my part. The way that I interpreted the definition given in Wikipedia's UXP article is that there are 2 errors, which I will cover here.
- The fourth condition requires that between (-1) and 0, UXP' is a:
"nondecreasing or nonincreasing" function, but this should read
"nondecreasing and nonincreasing", which means UXP' is a constant, which means UXP is a linear function.
- The closed form given in the article defines UXP as:
\( \text{uxp}_a(x) = \exp_a^{[x+1]}(\ (x)\ ) \), but this should read
\( \text{uxp}_a(x) = (\exp_a)^{\text{int}(x+1)}(\text{frac}(x+1)) \), because of how "frac" is implemented on some CASs, and because this is much more clear than how it is described.
I hope the actual reference is better than this...
Andrew Robbins