# Questions tagged [paradoxes]

Paradoxes are arguments which contradict logic or common sense, often by using false and implicit premises.

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### Questioning Russell's Paradox.

I was reading this article on Russell's Paradox and at the third para of first section it mentions $x \in x$ as the property or expression $P(x)$ meaning $A=\{x:\neg P(x)\}$ where, $P(x)=x \in x$. ...
1 vote
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### Is Curry's paradox caused by allowing definitions to implicitly assert existence?

Context: I'm studying the lambda-calculus and formal systems of logic, and it seems that the naive approach to extending the lambda-calculus into a higher-order logic leads to Curry's paradox (https://...
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### Measure, Integration, and Real Analysis by Sheldon Axler Exercise 14 of Chapter 2A

I am studying Measure, Integration, and Real Analysis by Sheldon Axler & working on Exercise 14 of Chapter 2A Here is the image: The claim is that the sum of all 3 colored shapes, is 90.5, while ...
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### Banach-Tarski Paradox: Extension with cycles

I am new to StackExchange so apologies if my question is poorly asked or does not abide by the standards. Referring to the 2016 edition of Tomkowicz and Wagons' book on the Banach-Tarski Paradox, ...
177 views

### If I ask a person if they can say "no" and they say "no", is this a paradox?

If I ask a person if they can say "no" and they say "no", is this a paradox? If they answer "no" it means they can't say "no", but they just said it
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### What is the flaw in the following analysis of the Sleeping Beauty Problem

The sleeping beauty problem is a famous problem where a coin is flipped and then a subject is put to sleep. If the coin was heads they will be awoken on Monday asked what their belief is that the ...
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### Can Markov Chains be used to Disprove the St Petersburg Paradox?

I am learning about the St Petersburg Paradox https://en.wikipedia.org/wiki/St._Petersburg_paradox - here is my attempt to summarize it: A fair coin is tossed at each stage. The initial stake begins ...
491 views

### Why Doesn't the St Petersburg Paradox Happen All the Time?

I am learning about the St Petersburg Paradox https://en.wikipedia.org/wiki/St._Petersburg_paradox - here is my attempt to summarize it: A fair coin is tossed at each stage. The initial stake begins ...
142 views

### (SOLVED) Monty Hall: the number of unknowns decreases but probabilities stay the same?

I recently got an explanation of the Monty Hall problem and I thought I understood it but after giving it more thought, it still looks wrong. Instead of using goats and doors, the example used a 52-...
144 views

### Expressing Numbers Without Any Decimal Presumptions

I have long been uncomfortable with how numbers in alternative bases are expressed. Alternative bases are marketed as transcending our arbitrary base-$10$ conventions, but I wonder if they really ...
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### Why does this solution to Russell's Paradox not have a contradiction?

Discrete Mathematics with Applications, 3rd ed., by Susanna Epp mentions that Russell's Paradox can be avoided by ensuring that any condition elements of a set are to satisfy must contain the ...
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1 vote
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### Curry’s paradox in Turing machine land?

Background There’s an excellent question on MathOverflow that talks about the following: imagine that $M$ is a TM that searches over all ZFC proofs and halts if and only if it finds a proof that it ...
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### Coupon Collector "Paradox"

Example Scenario: Imagine a Player has an unfair die with sides: $\{A,B,C,D,E,F\}$ The probability of each side $p_i = \{1/12,1/6,1/4,1/12,1/6,1/4\}$ The player's goal is to obtain at least one of ...
1 vote
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### Two boys paradox

I have a question regarding how to form the sample space in this famous paradox. Usually the sample space is defined as (B,B), (G,B), (B,G) and (G,G). However if I express it as (B1,B2), (G,B) and (G1,...
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### Why does Simpsons Paradox Happen in Real Life?

Here is a famous example of Simpsons Paradox about Kidney Stone treatments (https://en.wikipedia.org/wiki/Simpson%27s_paradox): ...
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