Reputed Austrian American mathematician Kurt Gödel formulated two extraordinary propositions in mathematical lo0gic.Accepted by all mathematicians they have revolutionized mathematics, showing that mathematical truth is more than logic and computation. These two ground breaking theorems changed mathematics, logic, and even the way we look at our Universe. The cognitive scientist Douglas Hofstadter described Gödel’s first incompleteness theorem as that in a formal axiomatic mathematical system there are propositions that can neither be proven nor disproven. The logician and mathematician Jean van Heijenoort summarizes that there are formulas that are neither provable nor disprovable. According to Peter Suber, inn a formal mathematical system, there are un decidable statements. S. M. Srivatsava formulates that formulations of number theory include undecidable propositions. And Miles Mathis describes Gödel’s first incompleteness theorem as that in a formal axiomatic mathematical system we can construct a statement which is neither true nor false. [Mathematical variance of liar’s paradox]In this short work, the author attempts to show these equivalent propositions to Gödel’s incompleteness theorems by applying elementary arithmetic operations, algebra and hyperbolic geometry. [1 – 6 ]
Comments: 4 Pages. If there is a flaw in the proof, I welcome it.Thank you.
[v1] 2015-04-24 03:39:05
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