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

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How can this paradox be resolved?

I came up with a (probably unoriginal) paradox today, and was wondering how it might be resolved. Its approach to reasoning seems to resemble basic game theory techniques. Suppose a casino game has ...
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How is the Liar Paradox a paradox?

In the Liar Paradox, someone says "I am a liar.", which we assume means "Everything I say is false." (although even that's not correct, a liar is defined as someone who says lies, not someone who only ...
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Is it a “paradox”, or a flaw in the question?

(Clearly not a pardox per-se but I would like to hear what you think) The basic riddle (not a very interesting one even) goes as follows: A first client comes into a barber shop, takes a hair cut ...
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Coin flips and prediction - Is this a paradox?

Let's say a coin is given to you which is shown to have two sides (head and tail). I threw the coin 10 times and I got the sequence HHHHHHHHHH (all heads). Now, I am about to throw it the eleventh ...
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How can a set contain itself?

In Russell's famous paradox ("Does the set of all sets which do not contain themselves contain itself?") he obviously makes the assumption that a set can contain itself. I do not understand how this ...
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resolving expected utility of st. petersburg paradox with logarithmic utility

St. Petersburg paradox is a game where you toss a fair coin repeatedly and if it lands heads on the $k$th trial you get $2^n$ dollars. Expected utility of game is: $E(U) = \sum_{k=1}^{\infty}[0.5*0 + ...
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mathematical limit for a ouroboros torus

The other day i was watching an episode of Tom and Jerry in which a similar situation was present toms head comes out of his own mouth. My head hurts when i think how is that even possible so i ...
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Pythagorean “Paradox” (right-angled triangle). [duplicate]

Consider an isosceles right-angled triangle as shown in the figure (top left). The length of its hypotenuse is $c$. The figure distinguishes both legs of the triangle, however, from now on let's ...
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Probability Paradoxes that Puzzle Professors.

There is a class of probability puzzles that includes Monty Hall/Three Prisoners, Three Cards/Pancakes, Two Children/Boy or Girl, their common antecedent Bertrand's Box Paradox, and (a more ...
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the answer for thomsons lamp?

Consider a lamp with a toggle switch. Flicking the switch once turns the lamp on. Another flick will turn the lamp off. Now suppose that there is a being able to perform the following task: starting a ...
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Explanation of two boxes problem? [duplicate]

Two piece of gold are contained in two same-looking black boxes respectively. It is known that one piece weights twice as the other, but do not know which is which. Two persons, say A and B, ...
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Birthday paradox in choosing random identifiers

If I have a network which has $n$ nodes and every node has an identifier. I want to find what is a sufficient value of $l$, which describes length of identifier, such that every node has different ...
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The sum of all the odd numbers to infinity [duplicate]

We have this sequence: S1: 1+2+3+4+5+6.. (to infinity) It has been demonstrated, that S1 = -1/12. Now, what happens if i multiply by a factor of 2? S2: 2+4+6+8+10+12.... (to infinity). I have ...
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Fallacy - where is the mistake?

Could anyone help me to find the mistake in this fallacy? Because the actual result for $I$ is $\pi/2$ \begin{equation} I = \int_{0}^{\pi} \cos^{2} x \; \textrm{d}x \end{equation} \begin{equation} I ...
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How would you explain this graph illustration of Simpson's paradox?

I need your help for understanding WHAT in the graph you find in the following link proves Simpson's Paradox. For those who don't know about Simpson's paradox, it is the inversion of the inequalities ...
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Points and real intervals [closed]

The sorites paradox goes like this: Start with a heap of sand. Remove a grain of sand and you still have a heap; remove another, and another, and another, and you'll still have a heap. Eventually, ...
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If you have two envelopes, and …

Suppose you're given two envelopes. Both envelopes have money in them, and you're told that one envelope has twice as much money as the other. Suppose you pick one of the envelopes. Should you switch ...
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Russell's paradox and axiom of separation

I don't quite understand how the axiom of separation resolves Russell's paradox in an entirely satisfactory way (without relying on other axioms). I see that it removes the immediate contradiction ...
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Why is Banach–Tarski's paradox so interesting?

Here is how I understand the Banach–Tarski paradox, based on the Wikipedia article : with a clever partitioning, one can decompose a solid ball into two solid balls, each identical to the first one. ...
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Hilbert's hotel with uncountably infinite rooms: can you fit $\mathbb R^2$ guests?

I'm trying to expand on Hilbert's paradox. The original version states that: Suppose there is a hotel with a countable infinity of rooms (eg. $\mathbb N$), all of which are occupied. ...
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Understanding the solution of a riddle about lions and sheep.

I heard a riddle once, which goes like this: There are N lions and 1 sheep in a field. All the lions really want to eat the sheep, but the problem is that if a lion eats a sheep, it becomes a sheep. ...
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If supposing that a statement is false gives rise to a paradox, does this prove that the statement is true?

The title pretty much says it all: If supposing that a statement is false gives rise to a paradox, does this prove that the statement is true? Edit: Let me attempt to be a little more precise: ...
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Dichotomy Paradox for the Running Man.

This question is inspired by the Dichotomy Paradox but with a twist: Let's say that Telemachus is running between two light posts, distance L length units apart. He starts at the first light post with ...
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Fixed point combinator and functions with no fixed point

In lambda calculus the fixed point combinator is defined as: It is very easy to see how $Yg =g(Yg)$ for any $g$ by using $\beta$-reduction. At the same time I wonder what is the meaning of ...
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Constructing a circle from a square [duplicate]

I have seen a [picture like this] several times: featuring a "troll proof" that $\pi=4$. Obviously the construction does not yield a circle, starting from a square, but how to rigorously and ...
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Demonstration that 0 = 1 [duplicate]

I have been proposed this enigma, but can't solve it. So here it is: $$\begin{align} e^{2 \pi i n} &= 1 \quad \forall n \in \mathbb{N} && (\times e) \tag{0} \\ e^{2 \pi i n + 1} &= e ...
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Explain probability paradox

I was planning my cycling schedule when I thought of this question... Can anyone explain why this is not true??? Suppose there is a 1% chance of a person getting knocked down by a vehicle each ...
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1answer
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“Waiter's paradox” - what's wrong with this reasoning? [duplicate]

Here's a puzzle I just heard and while I know that this reasoning is fundamentally wrong, I can't explain why: Three people bought a dish for, say, 25\$ and paid 30\$ The waiter didn't want to ...
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1answer
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Problems with nesting proof predicates in first order logic.

Whenever I start nesting proof predicates, I always seems to run into these bizarre situations. I was wondering if anyone knows about this and could shed some light on it or provide me with some ...
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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. ...