I understand that temperature has a lower bound of zero kelvin. Is this temperature actually achievable. If not, isn't zero kelvin just acting like negative infinity?
For example, say I come up with a new temperature unit. It will be related to Kelvin by just being the log. So $t = \log(k)$, where t is the new temperature, and k is the temperature in Kelvin.
T can range from $-\infty$ to $\infty$, thus there is no lower bound to this temperature measurement.
Similarly, I can make $u = 1/2 + \arctan(\log(k))/\pi$ to get a temperature measurement (0, 1). So now there is an absolute hot of 1 and absolute cold of 0..
Is there a reason that Kelvin is much better? Is it true that temperature having a lower bound but no upper bound is just a matter of "perspective"? Or is there something inherent about temperature that I am missing?