New Philosophical View Merging Infinity, Imaginary Number and Zero and a New Arithmetic Solving Indeterminants
- Author Salah A. Mabkhout
- DOI
- Country : Republic of Yemen
- Subject : Mathematics
Keywords : Philosophy of mathematics, Foundation s of Mathematics, Logic, Infinity, Imaginary numbers, Zero, Paradoxes, Indeterminants.
Abstract
If the expression i=√(-1) has a solution that is not a real number, what might be that? So the question is a philosophical and foundational one, simply to wonder about what we are dealing with. Concern about the foundations of mathematics therefore means that the problem of imaginary numbers is in fact a problem and cannot be dismissed as superfluous or trivial. What is the essence of =√(-1) ? We discover the very nature of i=√(-1) to be i=√(-1)=-∞. From Euler formula exp2πi=1, we deduce the imaginary phase of the zero, that is 0=2πi. Thus we tame the zero. We develop new axioms to tame infinity, zero and the imaginary number. Hence we develop a new arithmetic, solves the problem of indeterminants. Eventually, many paradoxes were resolved if infinity had taken to be both even and odd simultaneously.
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