Skip to main content

Questions tagged [paradoxes]

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

Filter by
Sorted by
Tagged with
-1 votes
0 answers
78 views

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$. ...
Mystic mystic's user avatar
1 vote
1 answer
73 views

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://...
Richard's user avatar
  • 41
0 votes
1 answer
55 views

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 ...
melon's user avatar
  • 11
0 votes
0 answers
68 views

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, ...
marcusmathematics's user avatar
5 votes
2 answers
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
Dottor Ivan's user avatar
3 votes
1 answer
145 views

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 ...
Jeff's user avatar
  • 873
0 votes
1 answer
92 views

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 ...
Uk rain troll's user avatar
8 votes
3 answers
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 ...
Uk rain troll's user avatar
0 votes
5 answers
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-...
moumous87's user avatar
-1 votes
1 answer
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 ...
user10478's user avatar
  • 1,912
3 votes
6 answers
287 views

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 ...
Cynicrom's user avatar
  • 316
1 vote
2 answers
143 views

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 ...
templatetypedef's user avatar
2 votes
1 answer
69 views

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 ...
TheRealOne's user avatar
1 vote
1 answer
84 views

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,...
jolulop's user avatar
  • 13
0 votes
0 answers
99 views

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): ...
Uk rain troll's user avatar
0 votes
1 answer
110 views

Number of rational numbers $\in (0,1) = $ number of rational numbers $\in (\frac{1}{2}$, 1)?

Let's say we have a set S of all rational number $\in (0,1)$. Now let us transform S to get a new set $S^{'}$ with the condition $x \in S \implies x + 1 \in S^{'}$. Now we again transform the set $S^{'...
Ham Lemon's user avatar
  • 619
0 votes
1 answer
111 views

The parabola paradox - how can this be thought of or visualized

One thing that has been hard to wrap my mind around- take a power function such as $x^2$ or $x^8$. I know the domain of x is infinite, unbounded. On the one hand such power functions increase in slope ...
gcr's user avatar
  • 127
1 vote
0 answers
34 views

Proving that we can define a paradoxical set in terms of equidecomposability.

I'm doing an undergrad project on the Banach-Tarski paradox and I'm not convinced by the proof I have come up with for this, everything to do with the Banach-Tarski Paradox is new maths to me and so I ...
spooleey's user avatar
  • 456
0 votes
0 answers
58 views

Variation of St. Petersburg Paradox

I was discussing the the St. Petersburg paradox and the following question came up: Suppose the game doesn't end within nine rounds, then the player directly receives $2^{10}$ dollars , while ...
Blue2001's user avatar
  • 371
0 votes
1 answer
68 views

Iteration paradox

I was got into a logical paradox. Can you resolve this paradox? An endofunction is a function whose domain and codomain is the same. For a positive integer $n$, define $R_n$ be a function which maps ...
imida k's user avatar
  • 295
1 vote
1 answer
121 views

A prize in 10 boxes

I am trying to make sense out of this experiment : There is a prize randomly put in one of 10 boxes. I am supposed to guess the box in which the prize lies. Q1: What is the sample space here ? Is it ...
Abhishek's user avatar
  • 135
1 vote
1 answer
112 views

Definition of classes

"We understand that a set is a collection of objects, but not every collection qualifies as a set, as exemplified by the collection of all sets (consider Russell's Paradox). To define the ...
Mousa Hamieh's user avatar
2 votes
2 answers
77 views

Contradiction about the set of all sets [duplicate]

How is it paradoxal that a set of all sets exists in set theory? Russel's paradox is about the set of all sets that do not contain themselves cannot exist, that I understand. But what about the set of ...
Brahim Khalil Abid's user avatar
1 vote
1 answer
261 views

What exactly are capture and release?

Motivation: I'm interested in how different people resolve the Liar paradox and other, related phenomena, like the revenge Liar paradoxes, and so on. I have a copy of "Formal Theories of Truth,&...
Shaun's user avatar
  • 45.5k
0 votes
3 answers
147 views

Bob has one sibling. What is the probability that he has a brother?

I've been thinking about this for at least a solid 30 minutes. I can't understand! I was looking at the 2 kids paradox (Tom has 2 children. At least one of them is a boy. What is the probability that ...
saganibadibik123's user avatar
1 vote
0 answers
139 views

Russels's Paradox: Well-defined collection of well-defined objects

The standard definition of a set is well-defined collection of objects. Here I assume that well-defined collection would mean any object is either a member of the collection or not. But if we take the ...
user221985's user avatar
3 votes
3 answers
2k views

What's the best explanation of the fallacy in this 'paradox'?

Of course whenever you have two statements that each on its own sound plausible but then contradict each other, you can simply check which one is false by e.g. drawing a picture. But I hope that ...
Vincent's user avatar
  • 10.7k
3 votes
0 answers
110 views

Does the universal set exist without allowing the concept of a set belonging to itself?

I have studied some elementary set theory and encountered a proof that a universal set containing everything cannot exist, as follows: Suppose, on the contrary, that there exists a set $\mathbb U$ ...
Arfin's user avatar
  • 1,445
0 votes
2 answers
86 views

General solution to PDE $xu_x + yu_y = 2xy$, why using characterics in non-parametric form I get an incorrect general solution?

I am trying to solve the PDE \begin{align} xu_x + yu_y = 2xy \end{align} using the method of characteristics. So the characteristic equations are \begin{align} \frac{dx}{x} = \frac{dy}{y} = \frac{du}{...
jaxolotl's user avatar
2 votes
6 answers
844 views

Can a conditional be both vacuously true and false?

Imagine the following conditional: If washing machines are humans, washing machines are quadrupeds. It seems to me that the truth value of the conditional as a whole is ambiguous. Since its ...
Sokito's user avatar
  • 37
0 votes
1 answer
44 views

How does the barber's paradox apply to the halting problem but not similar solvable problems

I am trying to understand Turing's halting problem proof by applying the same paradox to a similar problem where, instead of determining if a given code will halt, you instead determine if it will ...
Alex Breeze's user avatar
8 votes
2 answers
183 views

Does this paradox prove that the halting problem is undecidable?

A real number is said to be computable if a finite, terminating algorithm can compute it to arbitrary precision. Since algorithms are countable (for example, one may list all possible c programs in ...
Luca Blanchi's user avatar
1 vote
0 answers
25 views

Name for the paradox of conditioning on "equivalent" continuous random variables

I remember being shown the following example in class some time ago, but haven't been able to find any information about it on the internet. The paradox Let $(x, y)$ be a uniform random variable on ...
S. Dauncey's user avatar
4 votes
1 answer
277 views

Is there a name for this probabilistic paradox?

Let $X\sim Exp(1)$ and $Y\sim Exp(\lambda)$, independent. Then, \begin{align} f_{X|Y=mX}(x) = \frac{f_{X,Y}(x,mx) }{\int f_{X,Y}(x,mx) \:dx }=\frac{f_X(x)f_Y(mx) }{\int f_X(x)f_Y(mx) \:dx } = \frac{e^{...
Christopher Wu's user avatar
-3 votes
1 answer
204 views

Hilbert's Grand Hotel is always hosting the same infinite set of guests

I am learning the fundamentals of mathematics. A bit background: This article says that "The mathematical paradox about infinite sets" envisages Hilbert's Grand Hotel: "...a hotel with ...
Prudencio's user avatar
1 vote
0 answers
72 views

How do you explain this paradox in probability? A slight change in conditions doubles the probability!

The paradox is simple to explain but it really confuses me. Suppose X is the weight of a mango from a very large batch of mangoes. Let's say X is normally distributed with mean $= 300$g, so the ...
Jiaqi Luo's user avatar
0 votes
0 answers
57 views

How is Banach-Tarski paradox "more powerful" than Sierpinski-Mazurkiewicx paradox?

(1) Am I correct that the Banach-Tarski paradox (BT) was discovered before the Sierpinski-Mazurkiewicx paradox (SM)? (2) In many ways SM seems "more powerful" than BT. (a) It uses two pieces ...
James Dow Allen's user avatar
3 votes
1 answer
105 views

Self-referential paradox

In some legal documents, we read, "this page is intentionally left blank." Since this text is written on this page, the page is not really blank. Is there a mathematical formulation for this ...
zeynel's user avatar
  • 411
3 votes
1 answer
98 views

Can (a certain interpretation of) the Ross-Littlewood paradox be formalized in set theory?

In the Ross-Littlewood paradox, there is a supertask that goes as follows: At step 1, you add 10 balls to a jar labeled 1 through 10 and remove ball #1. At step 2, you add 10 balls to a jar labeled 11 ...
Maximal Ideal's user avatar
2 votes
1 answer
177 views

Being a member of a set in itself [duplicate]

Hello to all math lovers. I was studying Russell's paradox in set theory and came across something ambiguous that I couldn't justify no matter how hard I tried. The strange thing was: sets that are ...
Mostafa Zeinodini's user avatar
0 votes
3 answers
146 views

Proving $(1+x)^n\ge nx$ is easier by just proving $(1+x)^n\ge nx+1$. Exercise: explain this paradox

Chapter 6.3 in "How to prove it" by velleman has a theorem: The last exercise of the chapter asks the reader to explain what the paradox was in the proof: At first I thought it has something ...
bobbyJames's user avatar
0 votes
2 answers
513 views

Understanding the "Just one more" paradox on a logarithmic scale

I got somewhat puzzled after watching this video on Kelly Criterion in economics and the associated "just one more" paradox. This question should be self-contained, so watching the video ...
Aleksejs Fomins's user avatar
1 vote
1 answer
118 views

Sleeping beauty paradox variation favouring halfers

I have been reading about the Sleeping Beauty problem and I have been considering a slight variation to make the absurdity of the thirder position more apparent: Suppose we have a biased coin that ...
Daniel Wyatt's user avatar
0 votes
1 answer
120 views

Paradox regarding the size of real numbers? [closed]

Suppose you want to represent numbers in base 9, so digits 0 to 8. You can express any real number in base 9, so this set is uncountably infinite. However, it can be shown that in base 10, the ...
Buddy's user avatar
  • 119
1 vote
1 answer
45 views

Conditional probability when the given outcome has probability $0$

Consider two different random variables on $\{0,1\}^{\mathbb N}$, i.e. the set of binary sequences. The first random variable $X_1$ has a distribution defined by letting each of its digits be chosen ...
Franklin Pezzuti Dyer's user avatar
0 votes
0 answers
52 views

Differing probabilities in discrete vs continuous two-envelopes

Consider the famous two-envelopes problem, summarized below: A wealthy eccentric places two envelopes in front of you. She tells you that both envelopes contain money, and that one contains twice as ...
1110101001's user avatar
  • 4,198
-2 votes
4 answers
742 views

Is this "laziness contest" joke a paradox?

I stumbled across a seemingly paradoxical joke online that read: "when your opponent doesn't show up to the laziness contest" The joke is that you have already lost the contest by showing ...
Scene's user avatar
  • 1,601
2 votes
1 answer
189 views

Why is Russell's set non-well-founded?

It is usually said that the Russell set (the set $R$ of all sets that are not members of themselves) is non-well-founded, but I honestly do not understand why. If an object is non-well-founded, it ...
Fernanda's user avatar
0 votes
1 answer
106 views

Could you say that the unxepected hanging paradox is a falsidical paradox?

In Harrie de Swart book Philosophical and Mathematical Logic, Quine's classification of paradoxes to falsidical, veridical and antinomies paradoxes is explained. Then in exercise 2.70 we are asked to ...
Michael Novak's user avatar
2 votes
0 answers
343 views

Why should mathematics not allow contradictions?

Heads up. I have no technical training in logic, nor have read any book about it. This question is coming mostly from my intuition, so please consider giving me a reference --- I'm particularly ...
user1145880's user avatar

1
2 3 4 5
13