Final answer:
The Heisenberg Uncertainty Principle is both a mathematical and physical result of quantum theory's wave-particle duality, imposing fundamental limits on measurement precision for properties like position and momentum.
Step-by-step explanation:
The Heisenberg Uncertainty Principle is both a mathematical and physical consequence arising from the wave-particle duality foundational to quantum mechanics. This principle illustrates a fundamental limit to the precision with which certain pairs of physical properties, such as position and momentum, can be known.
The uncertainty is quantified by the equation ΔxΔp > h/4π, where Δx represents uncertainty in position and Δp represents uncertainty in momentum. In everyday life, we do not notice these effects because Planck's constant is extremely small, making the uncertainties for large objects negligible. This aligns with the correspondence principle, which posits that the predictions of quantum mechanics converge with those of classical mechanics for macroscopic systems.