The relationship between limits and motion? (Limits in calc)

[CalebB-M]

The first day of physics 211 (calculus based) at my school, our teacher started us out with dimensional analysis and it's importance. We started with the plank length which is in meters and while he didn't specify why, we used the plank constant ,gravitational constant, and the speed of light to find the length of a plank. This relates to my thought from limits in calculus. If we define a limit as infentesimally small point away from another. What does this imply that all of motion could be very accurate estimates ?. If we have a length (a plank) that is where macro physics breaks down doesn't that imply that our entire universe is fuzzy ? That all of reality is just slightly better estimates and that we don't have a true exact value for a position?
Note: this is just my thoughts and I would love to hear from both graduated physics majors as I am only a freshman.
Edit: sorry admins for the wrong section, thank you for moving my thread to a better spot!

 

[Khashishi]

Calculus has nothing to do with Planck length. You do not need to consider Planck length at all to apply limits. A differential is a purely mathematical object and has nothing to do with Planck length.

I'm not sure why your teacher decided to bring up Planck length. You won't need that number for any physics at an undergraduate level. The Planck length is very, very small. Classical physics breaks down way before you get that small. Quantum mechanics will answer some of your questions about "fuzziness", but even quantum mechanics probably breaks down around the Planck length, and you need a theory of quantum gravity, which is not something you will study in class, but rather a subject of advanced theoretical research.

 

[CalebB-M]

The actually lesson was only about analyzing units, but I decided to think more (even though I am completely wrong ) about the significance of magnitude. In essence I was just thinking out loud and trying to make connections that might not be there.
My full thought was probably worded improperly.
I guess I was thinking in my head if we can find values infinitely close to something could that mean that we could not define a true position to something in relation to another? Or is every value of position just an infinitely close enough value? That lead me to feel like all of the universe is a fuzzy line if you look really really close.
I realize I'm probably making no sense, but this is the learning stage.

 

[Khashishi]

There is uncertainty in position, but not because of calculus. There is no uncertainty in calculus. If you break things down into infinitely small pieces, it becomes exact.

 

[olivermsun]

I guess I was thinking in my head if we can find values infinitely close to something could that mean that we could not define a true position to something in relation to another?

In a way this is similar to a question in mathematics. Supposing you have two real numbers that are "infinitely close" together, are they the same number? The classical treatment says that they are. Hence if positions are expressible by real numbers, then I suppose infinitely close positions are the same position.

Or is every value of position just an infinitely close enough value? That lead me to feel like all of the universe is a fuzzy line if you look really really close.
I realize I'm probably making no sense, but this is the learning stage.

No problem. It's an interesting question. "Infinitely close" is usually taken to mean "closer than any finite number," in which case there can never be a "close enough" where you can tell the difference.