Bad math. Have you studied the calculus? Infinitesimals "exist"; we can add them and get something.
We’re not talking calculus. If there is no time that elapses between sinful to sinless, there’s no in between.
I would dare say if the amount of time is a blink of an eye, there is no purgatory. Changing instantly from having a sin nature to sinless, does not require an intermediate state called purgatory.
Besides that has never been how purgatory was described to me or anyone else growing up in the RCC. It was a place you spent hundreds or more years in, in purifying fire, to ‘take care’ of the sins you had committed before you died but didn’t do penance for. That is exactly how the nuns described it, that was how the priests described it. That was how my religious education teachers talked about it. It was most certainly NOT EVER, EVER talked about as being instantaneous; the entire emphasis about purgatory was that most people were going to be spending a great deal of time there. That was why we said masses for people. That’s why we prayed for people to get out of purgatory. They were still saying masses for people hundreds of years ago to help them get out of purgatory.
Anyway, we’re probably not far off in what both of us are discussing, and I am not truly interested in making a big deal over wording.