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location Tokyo, Japan
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visits member for 1 year, 2 months
seen Jul 12 at 13:49

Jul
12
accepted Prove that $\lfloor\lfloor x/2 \rfloor / 2 \rfloor = \lfloor x/4 \rfloor$
Jul
2
awarded  Curious
Jun
9
awarded  Yearling
Apr
23
awarded  Popular Question
Nov
25
awarded  Notable Question
Sep
28
awarded  Popular Question
Aug
9
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."
Aug
9
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?
Aug
9
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?
Aug
9
asked Are (some) axioms “unprovable truths” of Godel's Incompleteness Theorem?
Aug
6
accepted Where, specifically, did Principia Mathematica fail?
Aug
5
asked Where, specifically, did Principia Mathematica fail?
Aug
4
awarded  Critic
Aug
4
accepted Help understanding $x=y\Rightarrow(x=z\Rightarrow y=z)$
Aug
4
asked Help understanding $x=y\Rightarrow(x=z\Rightarrow y=z)$
Aug
2
comment What is the absolute minimum that must be accepted/defined in order to prove 1+1=2?
Awesome answer though, I just re-read it twice. I wonder, does the "traditional list" of axioms have a name?
Aug
2
comment What is the absolute minimum that must be accepted/defined in order to prove 1+1=2?
@dfeuer Of course as someone who will never be as skilled as you likely are in math, it might be out of place for me to say this, but I think you know what I'm asking for (at least, something more than just making 1+1=2 an axiom itself) and are instead just trying to immediately say the question is weak, without actually saying why it is weak, how it could be phrased better, and so on.
Aug
2
comment What is the absolute minimum that must be accepted/defined in order to prove 1+1=2?
It's good, it gives me something else to learn about.
Aug
2
asked What is the absolute minimum that must be accepted/defined in order to prove 1+1=2?
Aug
2
awarded  Editor