I’d been going to reply and say “butbutbutbut the only possible interpretation of ‘clock face’ that would make the cardinality not be 2^c would be that ‘clock face’ means ‘pair of clock-hand positions’, and that’s just ridiculous” … and then I looked at the rest of the thread and saw that that was apparently what JKC meant. My apologies.
EDITED to add: er, and actually there are perfectly reasonable interpretations that make the cardinality only the same as that of R, such as anything that can be described completely by a finite set of simple closed curves, or an RGB colouring where the colour at each point is a continuous function of position. So: total fail. Sorry again.
I’d been going to reply and say “butbutbutbut the only possible interpretation of ‘clock face’ that would make the cardinality not be 2^c would be that ‘clock face’ means ‘pair of clock-hand positions’, and that’s just ridiculous” … and then I looked at the rest of the thread and saw that that was apparently what JKC meant. My apologies.
EDITED to add: er, and actually there are perfectly reasonable interpretations that make the cardinality only the same as that of R, such as anything that can be described completely by a finite set of simple closed curves, or an RGB colouring where the colour at each point is a continuous function of position. So: total fail. Sorry again.