What's more exponential than \(e^{T}\)? \(e^{T^2}\), \(e^{T^{T}}\)?
Data for the following graph was not printable. \(T^T\) was too big. Although the graph was still presented by the spreadsheet program. The graph is just a series of data points from 1 to 15 on the x axis.
Temperature to the power of temperature. Which make \(0^0=1\) a testable reality. But
\(ln(n)=1\) makes \(n=e=2.718\)
Is this the minimum \(n\) for Bose-Einstein condensate? \(\lfloor n \rfloor=2\)?
For any other \(n\), \(Temp\ne0\); temperature simply cannot be zero. This suggests that Absolute Zero is attainable only with a pair of particles. We have not considered the gradient and y-intercept of the regression line.
If the gradient is \(A\) and the y-intercept is \(C\) then,
\(ln(n_{0})=A.0^0+C\), \(n_{0}=e^{A+C}\)
which could be any number. We are still in trouble if Absolute Zero is achievable only with a specific number of particles.
Goodnight.
