Questions tagged [paradoxes]
Paradoxes are arguments which contradict logic or common sense, often by using false and implicit premises.
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What's the name for an anti-paradox?
For example, take Russell's Paradox (does the set of all sets that do not contain themselves contain itself?). This is a paradox because answering the question with "yes" makes the answer &...
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Why this simple volume problem in Multivariate Calculus seems to have an anomaly?
Find the volume of the solid inside the cylinder $x^2+y^2-2ay = 0$ and between the plane $z = 0$ and the cone $x^2+y^2 = z^2$.
I tried solving this problem as follows:
Equation of the cylinder $x^2+(y-...
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Given a strong enough theory, why is $\operatorname{Richardian}(n)$ ill-defined?
Richard's paradox (on natural numbers) can be summarized as follows: Let $R$ be an enumeration of all the possible unary predicates that can apply to natural numbers. Perhaps, for example, $R_1(n) := ...
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expected value of the degree of a node's neighbor is larger than the expected value of the node's degree
Im trying to prove a certain property for the friendship paradox, which is basically showing that the expected degree of a node's friend is larger than the expected value of a node's degree.
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Minimum value mismatch
Say we want to minimize the sum $S = 9 + k^{2}$ which is clearly $9$.
But We know $(k-3)^{2} \geq 0$ Which gives $k^{2} + 9 \geq 6k$, so Minimum value of $S$ is $6k$ and clearly the equality holds ...
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Lack of strong law for the Saint Petersburg paradox
The Saint Petersburg paradox can be formulated as follows: Suppose we have a lottery whose payout ${X}$ takes taking values in the powers of two ${2,2^2,2^3,\dots}$ with
$\displaystyle {\bf P}( X = 2^...
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Partial derivatives of this function: it does exist but it doesn't.
I don't understand why I'm getting two different results about the existence of the partial derivative wrt $x$ of this function :
$$f(x, y) = \begin{cases} \frac{x^2+2y}{x^2+y^2} & (x, y) \neq (0, ...
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A wheel completes one rotation while the distance covered by the inner and outer circles are different [duplicate]
The wheel completes one rotation. By this time the outer circle covers $2\pi R$ distance while the inner circle covers $2\pi r$ distance. And obviously $2\pi R\ne 2\pi r$. But the initial and final ...
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Can the naïve version of Cantor's diagonal argument fail to find a number not on the list?
I was looking at a question here
How to resolve this paradox involving Cantor's diagonal argument?
This question was resolved by noticing that $1/9$ does not follow the pattern implied by the set ...
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How does the axiom of specification resolve Russell's paradox?
I've had some trouble understanding exactly how ZFC prevents Russell's paradox and most textbooks I read don't provide a justification for this. Up till now, here's my understanding.
Russell's paradox ...
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Determinism in Random Two Envelopes Paradox
The paper, “Pick the largest number”Open Problems in Communication and Computation Springer-Verlag, 1987, p152, deals with a version of the two envelopes problem where, after seeing one number, a ...
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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://...
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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 ...
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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, ...
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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
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