The paradox tag has no usage guidance.

**-5**

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66 views

### Infinite sum of n from 1 to infinity tend to -1/12 in String Theory? [on hold]

Why is this wrong result:
$$
\sum\limits_{n=1}^{\infty}n\rightarrow-\frac{1}{12}
$$
Used here: Volume I - String Theory - Joseph Polchinsky
Can someone explain its meaning in this book?
EDIT
I ...

**14**

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**0**answers

465 views

### Has anyone read/debunked Yessenin-Volpin–Hennix “Beware of the Gödel-Wette paradox”?

A student recently asked me about the status of a 2001 arXiv post, Beware of the Gödel-Wette paradox!, by Alexander Yessenin-Volpin (aka Esenin-Volpin and several other transliterations) and Catherine ...

**1**

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**0**answers

51 views

### A fixed point problem in infinite dimensions for monotonic algebras

Let $A$ be an algebra over $[0,1]$, whose operations are all unary monotone (increasing or decreasing) bijections, except that $A$ also includes the infimum operation over finite or countably many ...

**3**

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**2**answers

448 views

### Avoiding reflexive paradox in set theory

I am an amateur mathematician, and certainly not a set theorist, but there seems to me to be an easy way around the reflexive paradox: Add to set theory the primitive $A(x,y)$, which we may think of ...

**5**

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**5**answers

594 views

### Positive results coming from paradoxes

Many examples comes to mind, the most famous being the Gödel's theorems viewed as formalisations of the Liar's paradox. I just realised that the proof of non-calculability of Kolmogorov complexity is ...

**6**

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**5**answers

1k views

### How to tell a paradox from a “paradox”?

Russell's paradox showed that naive set theory leads to a contradiction. This was something that was taken seriously and caused a lot of work.
Now, Banach–Tarski paradox is arises from a result that ...