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20h
comment What kind of set-theory is sufficient to understand mathematical analysis?(book recommendation))
There is probably a lot of set theory you won't need. Don't worry too much about obtaining a contradiction. You can safely construct new sets from old sets by any of the following operations: (1) Selecting a subset of another set. Just don't refer to the new set in your selection criteria. (2) Obtaining the Cartesian Product of 2 or more sets. (3) Obtaining the power set of a set. (4) The pairwise union of two sets. (5) The union of a family of sets. (6) The axiom of choice to obtain a choice function. The most complicated. See: en.wikipedia.org/wiki/Axiom_of_choice#Statement
20h
comment What kind of set-theory is sufficient to understand mathematical analysis?(book recommendation))
For a quick introduction to formal logic and axiomatic set theory (the parts you may actually use in mathematical analysis), you may find useful the tutorial that comes with my proof checker available at dcproof.com
1d
revised Russell's paradox and axiom of separation
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revised Russell's paradox and axiom of separation
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revised Russell's paradox and axiom of separation
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revised Russell's paradox and axiom of separation
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revised Russell's paradox and axiom of separation
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revised Russell's paradox and axiom of separation
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answered Russell's paradox and axiom of separation
1d
comment What is the future of Set Theory if it is NOT the foundation of Mathematics?
See Andrej Bauer, "Univalent foundations subsume classical mathematics" at math.andrej.com/2014/01/13/… If so, then set theory is definitely NOT doomed.
May
18
comment Logic and Metamath book recommendation
You may find the tutorial that comes with my proof-checking software to be a useful introduction. Visit my website at dcproof.com The rules of logic used are a simplified version of standard FOL. They are easier to use and more in line with those implicitly used in mathematics textbooks.
May
14
comment Models of the successor function
There may be a first-order version of the induction axiom that accomplishes the same thing -- not sure
May
14
revised Models of the successor function
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May
14
answered Models of the successor function
May
14
comment This sentence is false
Hint: First, consider a slight variation: "This sentence is true." Though grammatically correct, it is obviously meaningless nonsense. Can changing "true" to "false" suddenly imbue it with meaning?
May
13
revised The necessity of the axiom of induction
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May
13
revised The necessity of the axiom of induction
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May
12
revised The necessity of the axiom of induction
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May
12
comment The necessity of the axiom of induction
You may find helpful the posting "What is a number again?" at my math blog dcproof.wordpress.com
May
12
answered The necessity of the axiom of induction