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Peter Smith's user avatar
Peter Smith's user avatar
Peter Smith's user avatar
Peter Smith
  • Member for 11 years, 11 months
  • Last seen this week
190 votes
Accepted

Why don't we define "imaginary" numbers for every "impossibility"?

82 votes

Prove that the union of countably many countable sets is countable.

62 votes

Fun but serious mathematics books to gift advanced undergraduates.

58 votes

We all use mathematical induction to prove results, but is there a proof of mathematical induction itself?

54 votes

Implies ($\Rightarrow$) vs. Entails ($\models$) vs. Provable ($\vdash$)

52 votes
Accepted

If $f(x)\leq f(f(x))$ for all $x$, is $x\leq f(x)$?

46 votes
Accepted

Textbooks on set theory

45 votes
Accepted

In proofs, are "for each" and "for any" synonyms?

34 votes
Accepted

Is $\forall x\,\exists y\, Q(x, y)$ the same as $\exists y\,\forall x\,Q(x, y)$?

34 votes
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Are the Gödel's incompleteness theorems valid for both classical and intuitionistic logic?

33 votes
Accepted

Logic nonsense/paradox

29 votes
Accepted

What is the prerequisite knowledge for learning Godel's incompleteness theorem

29 votes
Accepted

What is the purpose of free variables in first order logic?

28 votes
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First-order logic without equality

27 votes
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If it takes infinite steps to prove a statement, is that a valid proof?

25 votes
Accepted

How to find number of prime numbers up to to N?

25 votes

What axioms Gödel is using, if any?

24 votes

are there non-standard models of arithmetic in second order arithmetic?

24 votes
Accepted

what's the difference between Syntactic consequence ⊢ and Semantic consequence ⊨

23 votes
Accepted

How to interpret material conditional and explain it to freshmen?

23 votes
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Where, specifically, did Principia Mathematica fail?

22 votes

Is there a language that definitely won't have inconsistencies

21 votes

Can someone explain Gödel's incompleteness theorems in layman terms?

21 votes

Why are the rational numbers not continuous?

21 votes
Accepted

Confusion about mathematical writing?

21 votes
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Why do we believe the Church-Turing Thesis?

21 votes
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Modus Ponens: implication versus entailment

20 votes

Does mathematics require axioms?

20 votes
Accepted

Is the "domain of discourse" in axiomatic set theory also a "set"?

19 votes
Accepted

What's the problem this logic

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