CptSupermrkt
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 Apr2 awarded Popular Question Jan31 awarded Popular Question Jan20 awarded Nice Question Jan12 awarded Popular Question Sep14 awarded Popular Question Jul12 accepted Prove that $\lfloor\lfloor x/2 \rfloor / 2 \rfloor = \lfloor x/4 \rfloor$ Jul2 awarded Curious Jun9 awarded Yearling Apr23 awarded Popular Question Nov25 awarded Notable Question Sep28 awarded Popular Question Aug9 comment Are (some) axioms “unprovable truths” of Godel's Incompleteness Theorem? Maybe I'm using the word "true" incorrectly. Here's an example in my mind. Definition of water: a molecule made of hydrogen and oxygen. This is true/real/accurate. It can be "proven" because it can be seen (or can it? What does it mean to be seen?...). Basically my understanding of Godel's Theorems is that you can keep splitting hairs like this for eternity, but eventually you just simply have to stop and accept something. So I was just using basic axioms as an example, rather than the usual "barber's paradox" and "liars paradox." Aug9 comment Are (some) axioms “unprovable truths” of Godel's Incompleteness Theorem? @James But how can you have a definition if you are unable to prove that what the definition contains is true/real? Or CAN you prove what every definition contains? In which case I'm still stuck on my "0 is a natural number" axiom --- how can you prove that "0" is real, how can you prove that "natural numbers" are real? Aug9 comment Are (some) axioms “unprovable truths” of Godel's Incompleteness Theorem? @PVAL If any axiom has a proof for it in any logical system, what is the proof for the axiom that "0 is a natural number" in Peano's Postulates? Aug9 asked Are (some) axioms “unprovable truths” of Godel's Incompleteness Theorem? Aug6 accepted Where, specifically, did Principia Mathematica fail? Aug5 asked Where, specifically, did Principia Mathematica fail? Aug4 awarded Critic Aug4 accepted Help understanding $x=y\Rightarrow(x=z\Rightarrow y=z)$ Aug4 asked Help understanding $x=y\Rightarrow(x=z\Rightarrow y=z)$