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> integers exist

Mostly as an abstraction on top of a continuous wavefunction/quantum field

> Spacetime ends up being discretizable

As far as I know this is speculative and usually assumed by physicists to be false; it's definitely not a required feature of quantum mechanics per se, and as far as I know not of any other well-accepted theory.

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> Integers are fundamental in quantum mechanics, particularly as quantum numbers that define the discrete properties of particles, such as energy levels, angular momentum, and spin.

> Quantum mechanics dictates that certain properties, like energy and angular momentum, are quantized, meaning they can only exist in discrete packets or "quanta".

This was from a cursory google search.

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