Asaf Karagila

England

http://karagila.org

Born and raised in Israel. University Academic Fellow and UKRI Future Leaders Fellow at the University of Leeds. I mostly do some boolean combination of set theory, drinking, and being online.

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In (relatively) simple words: What is an inverse limit?

category-theory intuition universal-algebra limits-colimits asked May 11, 2011 at 18:11

math.stackexchange.com

155 votes

How To Present Mathematics To Non-Mathematicians?

soft-question big-list mathematics-education asked Nov 24, 2010 at 9:29

mathoverflow.net

111 votes

Why are infinitely dimensional vector spaces not isomorphic to their duals?

linear-algebra vector-spaces dual-spaces asked Aug 19, 2011 at 19:04

math.stackexchange.com

54 votes

How far are the $p$-adic numbers from being algebraically closed?

number-theory p-adic-number-theory asked Jan 7, 2011 at 22:49

math.stackexchange.com

50 votes

Does $2^X=2^Y\Rightarrow |X|=|Y|$ imply the axiom of choice?

set-theory lo.logic axiom-of-choice asked Nov 17, 2011 at 21:42

mathoverflow.net

49 votes

When does $A^A=2^A$ without the axiom of choice?

set-theory axiom-of-choice lo.logic asked Feb 24, 2013 at 5:43

mathoverflow.net

48 votes

How many algebraic closures can a field have?

set-theory fields axiom-of-choice asked Mar 19, 2019 at 9:41

mathoverflow.net

35 votes

What does the topology on $\operatorname{Spec}(R)$ tells us about $R$?

general-topology commutative-algebra ring-theory asked Feb 10, 2013 at 22:22

math.stackexchange.com

33 votes

Why algebraic closures?

abstract-algebra soft-question field-theory asked Jul 15, 2012 at 13:48

math.stackexchange.com

33 votes

Metrizable compactifications

general-topology metric-spaces compactness asked Sep 8, 2011 at 12:33

math.stackexchange.com

Top Answers

421

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

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192

Proofs that every mathematician should know.

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174

Why is compactness so important?

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156

"Simple" beautiful math proof

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127

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

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127

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

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121

Given real numbers: define integers?

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111

What is the difference between a class and a set?

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104

What are the Axiom of Choice and Axiom of Determinacy?

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104

Why did mathematicians take Russell's paradox seriously?

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102

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

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Which math paper maximizes the ratio (importance)/(length)?

mathoverflow.net

Is the axiom of choice really all that important?

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

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What is the definition of a set?

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

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Why don't analysts do category theory?

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

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Why is the Continuum Hypothesis (not) true?

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Results from abstract algebra which look wrong (but are true)

mathoverflow.net

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

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Too old to start math

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How do I prove that a function is well defined?

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

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Mathematical "urban legends"

mathoverflow.net

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

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How can a set contain itself?

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Infinite sets don't exist!?

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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.

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

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