In school I developed a strong hunch that continuity and infinity are "convenient delusions" we have that allow us to process the otherwise horrific complexity of the world. Experiencing time, sound, or visual motion as continuous, rather than discrete signal inputs is so much simpler. Similarly, the mathematical tricks and shortcuts we can use on well behaved continuous functions are both "unreasonably effective" and... probably not grounded in actual reality[1]? But damn are they convenient.

[1] EDIT: the reasoning is simple, if naive: the largest quantities we can measure are not, in fact, infinitely large, and the smallest ones we can measure are not, in fact, infinitesimally small. So until you show me an infinitesimal or an infinity, you're just making them up!

All math is made up. We've specifically made up math in a way which is useful to us.

You can make up math using different rules[1][2], and get different possibilities.

[1]: https://en.wikipedia.org/wiki/Non-standard_model_of_arithmet...

[2]: https://en.wikipedia.org/wiki/Internal_set_theory

I've always felt that to treat infinity as number is to commit a category error (aka type conflict), to confuse the process with the outcome of the process. Infinity has proven to be very useful, but usefulness doesn't make it always valid.

"All models are wrong but some are useful." -- George Box