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2 years ago in Foundational Mathematics , Mathematical Extensions By Debashis Mohapatra

What is 1/0 in mathematics?

Textbooks simply state "division by zero is undefined." But in calculus, we see limits approaching infinity, and in projective geometry, I've heard points at infinity. This seems like a contradiction. I'm trying to synthesize a coherent understanding: when is it absolutely forbidden, and when can we give it a meaningful interpretation?

Limit InputImpedanceCalculation ProjectiveGeometry

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By Riya N Answered 2 years ago

This is an excellent question that gets to the heart of how mathematical meaning is context-dependent. In the standard real number system, 1/0 is definitively undefined because division is defined as the inverse of multiplication, and no number times zero equals one. It's a permanent contradiction. However, I've worked in contexts where we assign it meaning. In complex analysis and projective geometry, we compactify spaces by adding a "point at infinity," allowing symbolic equations like 1/0 = ∞. But this ∞ isn't a number you calculate with; it's a conceptual boundary. So, it's forbidden in arithmetic but useful as a symbolic shorthand in more abstract settings.

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