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

learn more… | top users | synonyms (1)

3
votes
0answers
44 views

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. ...
3
votes
2answers
46 views

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: ...
2
votes
2answers
27 views

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 ...
2
votes
2answers
83 views

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 ...
0
votes
2answers
84 views

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 ...
24
votes
2answers
5k views

Demonstration that 0 = 1

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 ...
0
votes
1answer
42 views

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 ...
1
vote
1answer
44 views

“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 ...
3
votes
1answer
142 views

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 ...
2
votes
2answers
30 views

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 ...
0
votes
0answers
82 views

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)?
1
vote
1answer
79 views

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 ...
2
votes
2answers
95 views

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 ...
1
vote
0answers
34 views

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 $0$? ...
1
vote
2answers
121 views

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 ...
2
votes
1answer
58 views

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: ...
0
votes
1answer
50 views

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. ...
6
votes
3answers
333 views

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. ...
-1
votes
2answers
101 views

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 ...
2
votes
1answer
60 views

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 ...
0
votes
2answers
90 views

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 ...
0
votes
2answers
97 views

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.
1
vote
2answers
118 views

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 ...
0
votes
0answers
57 views

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 ...
1
vote
2answers
46 views

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 $Z=I(X=Y)$?
3
votes
2answers
47 views

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 ...
9
votes
0answers
189 views

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 ...
5
votes
0answers
72 views

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 ...
1
vote
0answers
65 views

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 ...
1
vote
1answer
86 views

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. ...
1
vote
4answers
453 views

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 ...
1
vote
0answers
116 views

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 ...
4
votes
3answers
190 views

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 ...
2
votes
1answer
85 views

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 ...
1
vote
2answers
88 views

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 ...
10
votes
3answers
261 views

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 ...
0
votes
3answers
171 views

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 ...
2
votes
2answers
93 views

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} = ...
16
votes
1answer
7k views

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), ...
2
votes
1answer
571 views

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 $b$. ...
1
vote
1answer
91 views

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?
2
votes
1answer
104 views

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 $E^*$ ...
3
votes
2answers
229 views

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 ...
0
votes
0answers
75 views

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 ...
3
votes
3answers
179 views

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 ...
3
votes
1answer
96 views

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?
3
votes
1answer
294 views

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, ...
2
votes
1answer
187 views

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 ...
3
votes
2answers
241 views

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 ...
3
votes
2answers
152 views

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 ...