Paradoxes are arguments, which are contradicting with logic or common sense, mostly using a false and implicit premises.

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Is there such a classification as Co-Paradox?

So, my line of thinking is that a set that contains all sets that do not contain themselves is a paradox. And the opposite of that is a set that contains all sets that contain themselves, and, while ...
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Understanding the Banach-Tarski Paradox

How is it possible to prove a paradox? Also, can someone explain the Banach-Tarski paradox in layman's terms (for someone up to calc 3 and ODEs knowledge)?
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How to make a good definiton

The reason why I come up this idea may due to Banach–Tarski paradox. The process we make a definition may consist of several steps. First step is that we observe a phenomenon. Second is to make a ...
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Formal approach to (countable) prisoners and hats problem.

I've found this nice puzzle about AC (I'm referring to the countable infinite case, with two colors). The puzzle has been discussed before on math.SE, but I can't find any description of what is ...
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Why is time important in the Ross-Littlewood paradox?

I have read many defferent versions of the Ross-Littlewood Paradox. This post: Fun quiz: where did the infinitely many candies come from? This post: Paradox: increasing sequence that goes to $0$? ...
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Fun quiz: where did the infinitely many candies come from?

Story 1: Let there be a bowl $A$ with countably infinite many of candies indexed by $\mathbb{N}$. Let bowl $B$ be empty. After $1/2$ unit of time, we take candy number 1 and 2 from $A$ and put ...
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St. Petersburg and the law of large numbers

Recently I learned about the discussion around the St. Petersburg paradox and how people try to explain why the calculated expected value differs so much from most people's intuition. My question: ...
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Are distance-related paradoxes limited by the size of an atom?

See these 2 paradoxes: Coastline paradox The coastline paradox is the counterintuitive observation that the coastline of a landmass does not have a well-defined length. ...
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Is the pseudomenon a statement?

I'm asking this because I'm teaching a class on paradoxes for kids, and I realized I have no idea what the answer to this question is. It is a research question in the pedagogical sense, I suppose. ...
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Does this paradox have a name?

As a student many years ago I learned of a paradox of something that is almost a certainty, while at the same time being highly improbable. For example, if you flip 10 coins the chances of all being ...
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Could you explain Perron's paradox to me, please?

This is Perron's paradox: Let $N$ be the largest integer. If $N > 1$, then $N^2 > N$, contradicting the definition of $N$. Hence $N = 1$. What does it mean? I get from it that a very large ...
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Russell's paradox with bounded comprehension

Consider the set $S = \{A, \varnothing\}$ and define $A = \{x \in S|x \not\in x\}$; this is the same as Russell's paradox except with bounded comprehension, ie $A\in A\iff A\not\in A$. I think the ...
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Could the birthday paradox be interpreted also about deaths?

Is the probability from the birthday paradox also true about deaths? If so, why? Or why not? I would think that it is also true about deaths, but it doesn't say so.
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Explain the Birthday Paradox

this is my first question at Maths Stackexchange, so, first of all, hello world! My question is, I recently read about the Birthday Paradox which states that in a group of 23 people, there's a ...
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World cup birthday paradox for two pairs

The BBC report on the world cup squads The birthday paradox at the World Cup shows the 50:50 prediction for there being 16 teams out of the 32 that meet the pair birthday criteria. However my ...
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An exercise about Borel paradox

If $X$ and $Y$ are independent standard normals, what is the conditional distribution of $Y$ given that $Z=1$, where $Z=I(X=Y)$?
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Paradox of the trumpet shape

This is a question I had for long time now, when you rotate the function y=1/x, x>0 (say x and y both measure meters) about the x axes by 2pi you get a shape which has infinite surface area and finite ...
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Paradoxical models of $\sf ZF$ without choice [closed]

There are some models of $\sf ZF$ without the Axiom of choice, where some paradoxical statements hold that are not possible in $\sf ZFC$ (we do not require that all those statements necessarily hold ...
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Connectedness of parts used in the Banach–Tarski paradox

A quote from the Wikipedia article "Axiom of choice": One example is the Banach–Tarski paradox which says that it is possible to decompose the 3-dimensional solid unit ball into finitely many ...
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Buffon needle in higher dimensions

Imagine a stick of length 1, and also a floor with evenly spaced lines, such that the distance between neighboring lines is also 1. If one throws the stick on the floor, there will be certain ...
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St. Petersburg Paradox. Expected value seems wrong.

Related: St. Petersburg Paradox I was reading today the Wikipedia page on the St. Petersburg Paradox. The posted expected value is: $ 1/2 * 1 + 1/4*2 + 1/8*4 ... $ This seems very wrong to me. ...
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Proof of Drinker paradox [duplicate]

I searched all over the internet but didn't find a formal proof for this paradox, so here is my attempt: $\exists x[P(x)\implies \forall yP(y)]$ Let $x=x_0$. Thus $P(x_0)$ is given. Let $y$ be ...
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Bus arrival poisson paradox

I have a question about the waiting time paradox for poisson processes(in this case in terms of bus arrivals). Suppose I know that buses arrive with poisson distribution(lambda). I arrive at fixed ...
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What exactly is the paradox in Zeno's paradox?

I have known about Zeno's paradox for some time now, but I have never really understood what exactly the paradox is. People always seem to have different explainations. From wikipedia: In the ...
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Very strange “fact” regarding movement

Perplexing (for me at least) statement from the site: http://www.quora.com/Mathematics/What-are-some-of-the-most-counterintuitive-mathematical-results "Fact: You can have a car stand still for ...
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Solving a version of the liar paradox

Given two people $Alice ,Bob$ are either lying or telling the truth Now suppose $Alice$ says "At least one of us is lying." We have two cases: $Alice$ is telling the truth $\implies$ $Bob$ is ...
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Elementary proof that there is no paradoxical decomposition using triangular pieces

I am teaching a geometry course and I am trying to understand two definitions in the textbook ("Geometry with Geometry Explorer" by Michael Hvidsten.) Definition: The area of a rectangle is its base ...
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Infinity and Hilbert's hotel paradox

I did some infinite series calculations while studying Fourier analysis and the concept of infinity really bugs me. I haven't read or heard not one sensible explanation yet (for me), what infinity ...
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Paradox with function representation

Let assume the function $\eta(E)$ has the following representation: $$\eta(E) = \sqrt{\frac{a}{E}}$$ where $a$ is the known positive constant, and $E \in [-\infty, +\infty]$. I know that $\sqrt{a} = ...
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Who discovered this number-guessing paradox?

In this math.se post I described in some detail a certain paradox, which I will summarize: $A$ writes two distinct numbers on slips of paper. $B$ selects one of the slips at random (equiprobably), ...
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Expected value of the distance between 2 uniformly distributed points on circle

I have the following problem (related to Bertrand): Given a circle of radius $a=1$. Choose 2 points randomly on the circle circumference. Then connect these points using a line with length $b$. ...
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Why $\bigcap \emptyset $ isn't defined? [duplicate]

Let us define: $\bigcap \emptyset = \{ x|\forall A(A \in \emptyset \Rightarrow x \in A)\} $ I understood that this cannot be defined. Somehow it enables Russell's paradox to exist. Why is that?
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Why is this inclusion of dual of Banach spaces wrong?

Ive been struggling the last days on this paradox, please I need help! Let $$E\subset F$$ be two Banach spaces equipped with the same norm. Some people told me that $$F^* \subset E^*$$ with $E^*$ ...
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How to ensure that you haven't run into a paradox proving a theorem e.g. by proof by contradiction?

While preparing some lecture notes for next semester and going back to basics (set theory and proof strategies) I came along the following simple question which is about proving theorems in general ...
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How to ensure that you haven't run into a paradox proving a theorem e.g. by proof by contradiction? [duplicate]

While preparing some lecture notes for next semester and going back to basics (set theory and proof strategies) I came along the following simple question which is about proving theorems in general ...
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Paradoxes in Logic

What is it that makes something a paradox? It seems to me that paradoxes are just, in many cases, misunderstandings about the properties some object can have and so misunderstandings about ...
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How can I understand is the picture $2D$ or $3D$

I can not understand is this picture 2D or 3D .what is the rule or condition to be a 2D or 3D picture.How can I understand that?please help me?
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On a scale of 1 to 10, how likely is it that this question is using binary? [closed]

I just read this interesting xkcd strip: At first I thought it was funny, but as I got to ruminate a little over it, I was surprised to be unable to find an answer. As Karolis Juodelė pointed out, ...
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Fingerprint match probability

I am trying to use the formula for the birthday paradox as a reference to figure out an equation that represents the probability of a fingerprint match. Here's the equation for probability of a ...
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Leibniz' Law and that good old riddle

There exists a Theory of Identity in mathematical logic. I've encountered it for the first time in Principia Mathematica by Alfred North Whitehead and Bertrand Russell (1910). Quote: "This definition ...
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Understanding: Axiom of Specification and Russell's Paradox: there is no universe?

Following Halmos's Naive Set Theory, Russell's Paradox emerges from using the axiom of specification (that for every set $A$ and property $\phi$ there exists a set $Y$ whose elements are those ...
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Notation in “proof sketch” of the Banach Tarski paradox on wikipedia

I'm trying to understand the proof sketch here. In step 3 of the proof sketch we have $A_{1} = S(a)M \cup M \cup B$. My understanding is that $S(a)$ and $M$ are both sets. I have failed to understand ...
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The set of all things. A thing itself?

If the universe is the set of all things. Does it contain itself? In other words is it a thing itself? I know its a stupid question, but it really grinds my gears. Thanks! Edit 8.12 Okey, someone ...
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Relationship between paradoxes in logic and geometry/topology

Though I've been reading for years, this is my first question here. Believe it or not, I've tried the search feature- apologies if this is a duplicate. The main point of this post can be summarized ...
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Why isn't $\int_0^1{1/x^2}~dx= 1$ + the integral from 1 to infinity.

This probably as nearly a stupid question as the one that isn't asked, but I've always thought the area under the curve is equal to the integral. So Given the function $\dfrac{1}{x^2}$ which is ...
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Mistake wikipedia article on St petersburg paradox?

I suspect that there is a mistake in the wikipedia article on the St petersburg paradox, and I would like to see if I am right before modifying the article. In the section "Solving the paradox", the ...
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Paradoxes in number theory

Does it exist any paradoxes within the field of number theory? Any examples? My thought is that since it is possible to find paradoxes in set theory, which in some sense more fundamental than number ...
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Variant on Russell's paradox: show $B = \varnothing$

Let $X$ be a set and $R$ a relationship on $X$. Define $N = \{x \in X\mid(x, x) \notin R\}$. Let $$B =\{b \in X\mid(\forall n \in N)(b\,R\,n) \land (\forall n \notin N)(\neg b\,R\,n)\}\;.$$ ...
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Simple tax puzzle

I recently saw some post on facebook whining about taxes. Simplifying it (and changing numbers, facts, etc.), this was saying: For each dollar an employer wants to pay you: 20% go in taxes that ...
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Is the answer to this question “no”? [closed]

The question in the title should be easy. So, yes or no?