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Questions tagged [paradoxes]

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

A paradox is an argument that produces an inconsistency, typically within logic or common sense. Most logical paradoxes are known to be invalid arguments but are still valuable in promoting critical thinking. However some have revealed errors in logic itself and have caused the rules of logic to be rewritten. (e.g. Russell's paradox)

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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 an initial velocity of V0. When he reaches L/2,…
V.Vocor
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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 it not decidable if it contains itself, neither…
user2063685
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What is the maximum number which can be written with fewer less than sixty five symbols?

If you try to write down all numbers with the symbols of any alphabet using at most 65 characters, then among them there must be a maximum. Let's call it $N$. But then the number described by the phrase "maximum number which can be written with…
aid78
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Zeno's Place Paradox

Zeno's Paradoxes are a series of problems intended to challenge our view of reality. Some of these paradoxes (e.g. Achilles and the Tortoise) have been disproven by a better understanding of physics and the concept of infinity. Here is his "Paradox…
Michael Wang
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Successive Bounces of Ball Paradox

Assume a Ball is bouncing and is travelling in the horizontal direction at constant horizontal velocity v. Also assume that after each successive bounce, the ball is is in the air for half the time of the previous bounce. We therefore conclude that…
Kenshin
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Berry's paradox with Godel encoding

I thought this is so obvious that people would have asked this question before, but for some reasons I can't find it. So here go: We are working in PA. With Godel encoding, we can encode a FOL formula as a number. Further more, given a number, there…
user336022
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"Waiter's paradox" - what's wrong with this reasoning?

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 divide 5 by 3, so he took 2\$ for himself and gave 1$…
d33tah
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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. Here is a game which would lead to the same expected…
Cruncher
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Russell's paradox and the barber paradox example

Russell's paradox deals with the set of all sets that do not contain themselves as a member of that set. It ask whether that set of all sets is also the member of the set or not. The barber paradox states :Consider a collection of barbers in a city…
math student
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Mathematical theories where paradoxes are formed from the assumptions of the system about itself

There are in fact certain paradoxes involved in the notion of a system that predicts its own behaviour. These are reminiscent of Russell's Paradox in set theory and of the paradoxes that arise when one allows a statement to talk about itself (e.g.,…
tryst with freedom
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choice set for equivalence classes

I'm trying to understand the proof of the Paradox of Banach-Tarski. I was reading Wagon's work about the paradox and tried to understand the proof of Theorem 1.5, only I haven't warmed up to group theory yet. Maybe someone can explain to me what…
user859080
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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 when the volume is 125cm$^3$" So the length $L$ of…
user2076694
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Finding the first program/algorithm with more than 1 million symbols in length which produces a new finite sequence within 1 trillion operations

Edit: There has to be an adjustment to my question as the number of permutations far exceeds 1 trillion which would lead to the main program doing way more than 1 trillion operations. Therefore, the number of operations allowed for the programs…
pZombie
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Does there exist a mathematical expression consisting of all mathematical expressions?

The set of all mathematical expressions consist of all analytic expressions, closed-form expressions, algebraic expressions, polynomial expressions, and arithmetic expressions. Do we run into Russell's paradox when talking about a set whose…
Cake
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What are "sets that don't contain itself" in Russell's paradox?

What are "sets that don't contain itself" in Russell's paradox? Since I think that for a set having to contain itself is intuitive and if a set doesn't contain itself, then the cardinality ought to be less than. However, I don't understand how sets…
mavavilj
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