User Patrick Stevens - Mathematics Stack Exchange

552 votes

Accepted

Why is $1 - \frac{1}{1 - \frac{1}{1 - \ldots}}$ not real?

answered Mar 3, 2016 at 20:58

126 votes

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What is lost when we move from reals to complex numbers?

answered Apr 8, 2018 at 20:36

68 votes

Abusing mathematical notation, are these examples of abuse?

answered Nov 5, 2017 at 13:33

63 votes

Mathematical ideas that took long to define rigorously

answered Feb 3, 2018 at 8:56

61 votes

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Why does Wolfram Alpha say that $\infty^\infty$ results in "complex infinity"?

answered Dec 31, 2016 at 19:39

48 votes

Intuitive explanation for why $\left(1-\frac1n\right)^n \to \frac1e$

answered Apr 5, 2016 at 10:42

32 votes

What is the exact difficulty in defining a point in Euclidean geometry?

answered Aug 9, 2016 at 10:36

29 votes

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True or false: {{∅}} ⊂ {∅,{∅}}

answered Aug 24, 2015 at 16:54

26 votes

Correct set notation for "all integers which are not multiples of 7"?

answered Mar 3, 2016 at 19:22

23 votes

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Mathematical notation $\max$ with simple example for non-mathematician

answered May 17, 2017 at 6:27

22 votes

Why is this seemingly valid argument using modus tollens not valid? How is this an example of "begging the question"?

answered Mar 25, 2017 at 8:55

20 votes

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Logical proposition for "Every positive integer can be written as the sum of 2 squares"

answered Aug 8, 2016 at 9:27

20 votes

Why does a product $\lim_{n\to\infty} \prod_{i=1}^n (1- \frac{1}{n+2i})$ lead to infinity?

answered Apr 3 at 20:38

19 votes

Similar Matrices and their Jordan Canonical Forms

answered Aug 23, 2015 at 18:33

18 votes

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Can an open set contain its supremum?

answered Apr 4, 2016 at 20:34

18 votes

How does modular arithmetic work - Fermat's last theorem near misses?

answered Dec 8, 2016 at 18:55

18 votes

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Why does "guess and verify technique" not involve circular reasoning?

answered Jul 10, 2017 at 0:54

18 votes

What is an example of a proof by minimal counterexample?

answered Nov 17, 2018 at 19:16

17 votes

What is exactly the difference between a definition and an axiom?

answered Sep 9, 2015 at 16:03

16 votes

Strategy for reading math books, is it better to prove the theorems yourself or just read them?

answered Aug 28, 2015 at 11:32

16 votes

Accepted

Do Gödel numbers have a practical use?

answered May 29, 2016 at 18:40

16 votes

What is a Universal Construction in Category Theory?

answered Mar 16, 2017 at 8:56

16 votes

Do direct sums commute with colimits?

answered Mar 2, 2017 at 21:58

16 votes

Accepted

Which branch of mathematics rigorously defines infinitesimals?

answered Feb 17, 2018 at 9:59

15 votes

When is a proof or definition formal?

answered Apr 6, 2017 at 7:07

15 votes

Prove $\sum\limits_{j=1}^k(-1)^{k-j}j^k\binom{k}{j}=k!$

answered May 22, 2016 at 11:45

15 votes

Is Cramer's rule efficient for computational point of view?

answered Oct 6, 2015 at 11:49

13 votes

Examples of a categories without products

answered Feb 3, 2016 at 7:57

12 votes

Accepted

Does a closed form solution exist for $x$?

answered Mar 16, 2016 at 0:25

12 votes

Why is wolfram alpha plotting this differently?

answered Apr 14, 2016 at 7:52

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981 Answers

Why is $1 - \frac{1}{1 - \frac{1}{1 - \ldots}}$ not real?

What is lost when we move from reals to complex numbers?

Abusing mathematical notation, are these examples of abuse?

Mathematical ideas that took long to define rigorously

Why does Wolfram Alpha say that $\infty^\infty$ results in "complex infinity"?

Intuitive explanation for why $\left(1-\frac1n\right)^n \to \frac1e$

What is the exact difficulty in defining a point in Euclidean geometry?

True or false: {{∅}} ⊂ {∅,{∅}}

Correct set notation for "all integers which are not multiples of 7"?

Mathematical notation $\max$ with simple example for non-mathematician

Why is this seemingly valid argument using modus tollens not valid? How is this an example of "begging the question"?

Logical proposition for "Every positive integer can be written as the sum of 2 squares"

Why does a product $\lim_{n\to\infty} \prod_{i=1}^n (1- \frac{1}{n+2i})$ lead to infinity?

Similar Matrices and their Jordan Canonical Forms

Can an open set contain its supremum?

How does modular arithmetic work - Fermat's last theorem near misses?

Why does "guess and verify technique" not involve circular reasoning?

What is an example of a proof by minimal counterexample?

What is exactly the difference between a definition and an axiom?

Strategy for reading math books, is it better to prove the theorems yourself or just read them?

Do Gödel numbers have a practical use?

What is a Universal Construction in Category Theory?

Do direct sums commute with colimits?

Which branch of mathematics rigorously defines infinitesimals?

When is a proof or definition formal?

Prove $\sum\limits_{j=1}^k(-1)^{k-j}j^k\binom{k}{j}=k!$

Is Cramer's rule efficient for computational point of view?

Examples of a categories without products

Does a closed form solution exist for $x$?

Why is wolfram alpha plotting this differently?