User Asaf Karagila

421 votes

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How do I convince someone that $1+1=2$ may not necessarily be true?

answered Nov 23, 2012 at 9:40

192 votes

Proofs that every mathematician should know.

answered Aug 5, 2012 at 11:40

174 votes

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Why is compactness so important?

answered Sep 6, 2013 at 16:00

156 votes

"Simple" beautiful math proof

answered Mar 26, 2014 at 22:20

127 votes

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What are the differences between class, set, family, and collection?

answered Jul 19, 2012 at 20:27

127 votes

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Is $|1-i|$ larger than $|1|$?

answered Feb 25, 2013 at 23:04

121 votes

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Given real numbers: define integers?

answered Dec 21, 2012 at 15:27

111 votes

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What is the difference between a class and a set?

answered May 1, 2012 at 10:32

104 votes

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Why did mathematicians take Russell's paradox seriously?

answered Mar 2, 2011 at 0:07

104 votes

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What are the Axiom of Choice and Axiom of Determinacy?

answered Jul 20, 2011 at 8:39

102 votes

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How do we know an $ \aleph_1 $ exists at all?

answered Jun 22, 2011 at 6:20

96 votes

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Is the axiom of choice really all that important?

answered Apr 27, 2015 at 4:06

90 votes

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What is the definition of a set?

answered Sep 26, 2015 at 17:19

90 votes

How would one be able to prove mathematically that $1+1 = 2$?

answered Dec 29, 2011 at 23:23

89 votes

Why don't analysts do category theory?

answered Jul 10, 2012 at 21:20

89 votes

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

answered Jul 27, 2013 at 16:42

77 votes

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What does it mean for a set to have Lebesgue measure zero?

answered Oct 25, 2017 at 10:56

77 votes

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Why is the Continuum Hypothesis (not) true?

answered Sep 1, 2012 at 0:44

74 votes

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Does $1.0000000000\cdots 1$ with an infinite number of $0$ in it exist?

answered Oct 18, 2014 at 8:51

73 votes

Too old to start math

answered Nov 14, 2012 at 12:56

70 votes

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How do I prove that a function is well defined?

answered Feb 24, 2013 at 18:36

70 votes

Why is "the set of all sets" a paradox, in layman's terms?

answered Aug 26, 2014 at 13:29

68 votes

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Is it possible to define countability without referring the natural numbers?

answered Mar 12, 2017 at 11:49

67 votes

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How can a set contain itself?

answered Dec 1, 2014 at 18:04

65 votes

Infinite sets don't exist!?

answered Apr 9, 2013 at 19:44

64 votes

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Axiom of Choice: Where does my argument for proving the axiom of choice fail? Help me understand why this is an axiom, and not a theorem.

answered Jun 26, 2016 at 6:00

63 votes

What was the first bit of mathematics that made you realize that math is beautiful? (For children's book)

answered Mar 7, 2013 at 7:29

62 votes

Accepted

What is the advantage of accepting the axiom of choice over other axioms?

answered Mar 16, 2012 at 14:21

60 votes

What is the most unusual proof you know that $\sqrt{2}$ is irrational?

answered Jun 3, 2015 at 22:54

60 votes

Accepted

Nonexistence of an injective $C^1$ map between $\mathbb R^2$ and $\mathbb R$

answered Aug 31, 2012 at 16:16

Stack Exchange Network

6,527 Answers

How do I convince someone that $1+1=2$ may not necessarily be true?

Proofs that every mathematician should know.

Why is compactness so important?

"Simple" beautiful math proof

What are the differences between class, set, family, and collection?

Is $|1-i|$ larger than $|1|$?

Given real numbers: define integers?

What is the difference between a class and a set?

Why did mathematicians take Russell's paradox seriously?

What are the Axiom of Choice and Axiom of Determinacy?

How do we know an $ \aleph_1 $ exists at all?

Is the axiom of choice really all that important?

What is the definition of a set?

How would one be able to prove mathematically that $1+1 = 2$?

Why don't analysts do category theory?

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

What does it mean for a set to have Lebesgue measure zero?

Why is the Continuum Hypothesis (not) true?

Does $1.0000000000\cdots 1$ with an infinite number of $0$ in it exist?

Too old to start math

How do I prove that a function is well defined?

Why is "the set of all sets" a paradox, in layman's terms?

Is it possible to define countability without referring the natural numbers?

How can a set contain itself?

Infinite sets don't exist!?

Axiom of Choice: Where does my argument for proving the axiom of choice fail? Help me understand why this is an axiom, and not a theorem.

What was the first bit of mathematics that made you realize that math is beautiful? (For children's book)

What is the advantage of accepting the axiom of choice over other axioms?

What is the most unusual proof you know that $\sqrt{2}$ is irrational?

Nonexistence of an injective $C^1$ map between $\mathbb R^2$ and $\mathbb R$