Division by zero, specifically 0, has been considered undefined due to its indeterminate nature [1]. In this paper, we propose treating 0 as an indeterminate state U, which belongs to a set of undefined states S. Drawing an analogy with quantum mechanics, specifically the concepts of superposition and wavefunction collapse [2, 3], we explore how such mathematical indeterminacies might behave similarly to quantum states prior to measurement. We introduce several types of"collapse"—conjugate, symmetric, asymmetric, and random—to describe the potential resolutionsof U into definite states. The framework presented here demonstrates mathematical consistency in representing and manipulating indeterminacies through (U1·0) = U2. Additionally, we propose hypotheses connecting this framework to quantum phenomena such as entanglement, the uncertainty principle, and cosmological singularities, suggesting that this approach may offer new insights into both mathematics and quantum theory.