Discontinuous Analysis

Hey, check my Discontinuous Analysis book. Its applications range from simplifying usual engineering calculations to new concepts in General Relativity and Quantum Gravity. I do this by defining "generalized limit" defined for all functions (provided suitable topological structure in the domain and image) at every point. "No limit for all functions at every point? No square root of -1? There is (in a wider space)." Generalized limit allows to easily define derivative for all functions at every point, integral of every function, and sum of any series (no, in my notation, 1+2+3+... != -1/12, it is a proper infinity). This theory greatly helps to simplify usual engineering calculations, because you don't need, for example, to check that a derivative exist and can cancel f'(x) - f'(x) = 0 without first checking for existence. Second, I make certain General Relativity (with my space of generalized limits instead of real number values) and quantum gravity conjectures. Solve them and share a Nobel Prize with me. Probably, we have another explanation of quantum information paradox than Hawking radiation. Does Hawking radiation even exist?

Sounds like a very intriguing book. Haven’t had the chance to dive deep into it yet, but the concepts look groundbreaking. Congrats on the release!