I understand what you're saying, but at the same time floating point numbers can only represent a fixed amount of precision. You can't, for example, represent Pi with a floating point. Or 1/3. And certain operations with floating point numbers with lots of decimals will always result in some precision being lost.

They are deterministic, and they follow clear rules, but they can't represent every number with full precision. I think that's a pretty good analogy for LLMs - they can't always represent or manipulate ideas with the same precision that a human can.

It's no more or less a good analogy than any other numerical or computational algorithm.

They're a fixed precision format. That doesn't mean they're ambiguous. They can be used ambiguously, but it isn't inevitable. Tools like interval arithmetic can mitigate this to a considerable extent.

Representing a number like pi to arbitrary precision isn't the purpose of a fixed precision format like IEEE754. It can be used to represent, say, 16 digits of pi, which is used to great effect in something like a discrete Fourier transform or many other scientific computations.