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

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I love to dance, and one of my favorite dances is the Waltz, and a beautiful waltz to dance to is “The Tennessee Waltz” which was a monster hit for Patti Page in 1950. An unusual feature of this song ...
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Banach-Tarski paradox in a countable set?

Let $M$ be a countable set. I can take a finite set $F$ of n-ary operations and construct a minimal set $M'$ for which: $M \subset M'$ For each $f \in F$ and $m_1,m_2…m_n \in M$ where $n$ is the ...
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Why does the comparison test fail here?

Someone recently stumped me here. Consider the series $\sum_3^{\infty} \dfrac{1}{x^{1.0001}}$ and the series $\sum_3^{\infty} \dfrac{1}{x\ln{x}}$. The first series in convergent, and the second ...
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I do not understand how the contraposition "all non-black objects are not ravens" is logically identical to "all ravens are black." I see that IF all ravens are black, THEN all non-black objects are ...
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Prove the sequence $\{ 2^n \}$ is unbounded using Russell's paradox

I am really stuck on how to make use of Russel's Paradox. This is where I started. Proof by contradiction. Suppose $\{ 2^n \}$ converges then it is bounded. Let $M$ be an element of the reals and a ...
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Attempting to prove $\int_0^{\infty} \frac{1}{x} dx$ converges

I'm sure countless people has tried to prove this but this is how I came across this, although I do remember seeing this in the past. Background https://www.youtube.com/watch?v=vQ0himyDR2E I was ...
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Brainteaser question/solution which reasonment is correct and why?

I am struggling to find some explanation to this: here is my problem: "A cube of ice melts without changing shape at uniform rate 4cm$^3$/min. Find the rate of change of the surface area of the cube ...
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The paradox of random occurrence the family problem

we have 100 families: 10 families have no children, 40 families have 1 child for each one, 30 families have 2 children for each one, 10 families have 3 children for each one and 10 families have 4 ...
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Is there a mathematical proof regarding Olber's Paradox? For me this feels a false paradox as I think that it IS possible to have an infinite (in space and in time) Universe with an infinite number ...
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Let's say that a finite probability space $(\Omega,\mathscr P(\Omega),P)$ has Simpson's property if you can find events $A,B,C\in\mathscr P(\Omega)$ such that $P(C) \in (0,1)$. $A$ and $B$ are ...
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Are there paradoxical/ counter-intuitive laws in predicate logic? ( beyond the Drinker Paradox)

Preliminary remarks. (1) The term "paradoxical" is not used in a negative sense here. What is " para-doxical" is literally what disagrees with the general and uninformed " opinion": it could be argued ...
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The proof of Banach-Tarski paradox on Wikipedia

https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox#Step_3 In the part of the proof that deals with the fixed points on $S^2$, the page says "Let $\lambda$ be some line through the origin ...
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Self-referential multiple-choice question [duplicate]

I came across this question, which I believe cannot be satisfactorily answered, but I'm not completely sure. Can you tell me if it has a answer? ...
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The Brandenburger-Keisler paradox runs as follows. 1) Suppose that A believes that B assumes that A believes that B's assumption is wrong 2) Ask whether A believes that B's assumption is wrong 3.1) ...
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I have been reading Halmos' book, Naive Set Theory and while reading the part about Russell's paradox I had the following question: Halmos shows that nothing can contain everything, as he puts it, but ...
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In the Stanford Encyclopedia's page on Russell's Paradox, we get the following anecdote about an additional, lesser-known paradox from Russell: ...in Appendix B Russell also presents another ...
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Independent events in the context of Simpson's Paradox

I came across this problem in the book "Introduction to Probability" by Dr. Joseph K. Blitzstein and Dr. Jessica Hwang. This problem deals with the concept of independent events in the context of the ...
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Can someone explain Wittgenstein's response to Russell's paradox in the Tractatus? Is it possible to cast the response as a mathematical proof? All explanations I have found so far mix logical and ...