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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n power 0, logarithm

This might appear like a unusual question, but I'd like to know how you can assume that $n^0 = 1$. If $y$ is the sum of $n$ multiplied by itself $x-1$ times, then the first power of a number is just the same number with no multiplication, and the…
Jnux
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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 complicated variation) Tuesday Boy. Any one of them will…
JeffJo
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false implication imples truth of any premise

I have dilemma with false implication. Say implication $A\to B$ is false, then this means that $A$ is true right? (based on truth table) So I am confused how in practice from false conclusion you can prove that any premise is true? Examples. If Jon…
dan
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St Petersburg paradox, can't replicate max lottery price on wikipedia

I've tried to verify the below statements on wikipedia because I think they're mixed up: https://en.wikipedia.org/wiki/St._Petersburg_paradox#Expected_utility_theory "For example, with log utility a millionaire should be willing to pay up to…
keithphw
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Hard time on understanding real analysis.

I am learning real analysis now but I really dislike the notion of limit, infinity... They seems to generate lots of paradoxes and unreasonable results. For example, when I am reading the uniform continuous notion, there is an example I find quite…
Y. Si
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The sum of all the odd numbers to infinity

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 2S1, which is equal to -1/6 On this, we can create a…
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Hilbert Hotel Paradox

In a video created by famous science blogger Veritasiuam(The Video), it explained the paradox, what to do if a finite number of guests come, what to do if even an infinite long bus of guests come, what to do if infinitely many infinitely long buses…
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Is this a solution to Russell's paradox?

Wikipedia says "Let R be the set of all sets that are not members of themselves. If R is not a member of itself, then its definition dictates that it must contain itself, and if it contains itself, then it contradicts its own definition as the set…
Yukang Jiang
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Basic math paradox

$1 = 1$ $ 1^2 = 1$ and $(-1)^2 = 1$ Therefore, $1^2 = (-1)^2$ Square root both sides $\sqrt{1^2} = \sqrt{(-1)^2}$ Therefore, $-1 =1$ This is an obvious paradox, but I don't know how to approach solving it
potapeno
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How would you solve this paradox?

Three friends walk into a bar, sit down, and when waiter comes to them, they ask him how much is the beer. The waiter tells them that the beer is $10$ dollars. They order three beers and each of them gives him $10$ dollars. A few moments later the…
Farewell
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How many $9$'s are there in $0.999\dots$ in the first $n$ places after the decimal point?

I am counting the number of $9$'s that will come in the first $n$ digits after the decimal point in $0.999\dots$ How many $9$'s will be there? For example, if I take $0.333\dots$ we will have $n$ number of $3$'s if I count them $n$ places after the…
Manish Khokhar
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