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"use strict";(self.webpackChunkfezcodex=self.webpackChunkfezcodex||[]).push([[271],{80271(e,t,s){s.r(t),s.d(t,{default:()=>i});s(9950);var n=s(44414);function i(){return(0,n.jsxs)("div",{className:"space-y-6 font-mono text-sm leading-relaxed",children:[(0,n.jsxs)("p",{children:["G\xf6del's ",(0,n.jsx)("strong",{className:"text-current",children:"Incompleteness Theorems"})," are two mathematical theorems proving inherent limitations in every formal axiomatic system capable of modeling basic arithmetic."]}),(0,n.jsx)("div",{className:"border-l-2 border-emerald-500/50 pl-4 py-1 italic opacity-70 text-xs",children:'"This statement cannot be proven."'}),(0,n.jsx)("p",{children:"The core implications:"}),(0,n.jsxs)("ul",{className:"space-y-2 text-xs opacity-80 list-disc pl-4",children:[(0,n.jsxs)("li",{children:[(0,n.jsx)("strong",{children:"First Theorem:"})," Any consistent formal system that is complex enough to do arithmetic will contain statements that are true, but cannot be proven within that system."]}),(0,n.jsxs)("li",{children:[(0,n.jsx)("strong",{children:"Second Theorem:"})," Such a system cannot demonstrate its own consistency. It cannot prove that it won't produce a contradiction."]}),(0,n.jsxs)("li",{children:[(0,n.jsx)("strong",{children:"The End of the Dream:"})," This destroyed the early 20th-century mathematical dream (championed by David Hilbert) of creating a single, complete, and perfectly consistent set of rules for all of mathematics."]})]})]})}}}]);