Abstract

This paper introduces the Infinity Definition Method a foundational redefinition of structure in mathematics. By adopting the symbolic identities \[ \frac{1}{\infty} = 0 \quad \text{and} \quad \frac{1}{0} = \infty \] as axiomatic, the method reconceptualizes arithmetic, limits, and equality. We examine the latent role of \( \frac{1}{\infty} = 0 \) in convergent series and unveil the hidden symmetry in limit operations where \(\sqrt{1}= 0 \) is implied structurally.