What is a good example of a paradox?

A nice example of a paradox I find that of the dollar machine thought-experiment.

Suggest that there was a dollar machine, which can print ten dollar bills at a time.Then imagine that we have a digital stopwatch, which enables us to be able to measure very accurately to infinity. We now set that stopwatch to [matht =-1 [/math.

Next, for each integer [mathn [/math, print the printer at time [matht =-\\frac{1}{n} [/math ten dollar bills.This means that the printer is at time [math-1 [/math, [Math\\frac {-1} {2} [/math, [Math\\frac {-1} {3} [/math, [Math\\frac {-1 } {4} [/math, etc.Ten dollar bills. Hopefully it doesn’t take much effort to understand that[matht = 0 [/math has printed the printer infinitely often (after all, there have been infinitely many times when the printer has been mounted.) and so that the printer also has infinitely many dollar bills Has printed.

If you have not fully understood the latter, it may be useful to draw a timeline with on the left [math-1 [/math and on the right side [Math0 [/math and then to put a line on the timeline, where and when the printer 10 new dollar bills press.(You will see that you can do that boundless often, but you still get closer to [matht = 0 [/math .At [matht = 0 [/math we say that the printer is ready and has infinitely many dollar bills printed.)

Note the number of infinite dollar bills itself is not yet the paradox; That has yet to come!

Because I like to live ordered, I decided to write a number on each dollar bill according to the place in the order in which the banknote was printed.So I write on the first dollar bill the number 1, on the second 2, on the third 3, etc. All dollar bills printed at time-1 then have a number from 1 to 10, at time-1/2 from 11 till 20 etc… For instance, each banknote can be assigned a number ad infinitum.

I am of course a dire opportunist and see in this dollar machine a fantastic opportunity to raise my standard of living.I would therefore like to take the ten dollar banknotes printed at any time. However, I am not just selfish and decide to share it with you as a reader in this fortune. At any time I put the ten dollar bills nine in my own pocket and I give one to you, I do as follows. At time [matht =-1 [/math I give you note number 1 and I insert number 2 through 10 in my pocket.At time [math t = \\frac{-1}{2} [/math I take note number 2 out of your own pocket, give it to you and I love about 3 to 20. At time [matht = \\frac{-1}{3} [/math I get out of my Pocket ticket number 3, give it to you and I keep about 4 to 30. Anyhow, you will hopefully understand the principle.

This is where the paradox comes into sniping.Competitive as both you and reader, as I am, we are both curious who is the richest after this fantastic deal. You wonder who is at time [matht = 0 [/math has the most dollar bills.Perhaps you are convinced that I am the richest of us both, because at every conceivable time I have put 9 times as many dollar bills in my pocket as I have given to you. Perhaps you say that we are both equally rich, because we both have infinitely many dollar bills and the cardinality of these infinite sets are equally great and that we both have equally many infinite notes in our pocket. However, nothing is less….

It turns out I’ve been guller, than I intended.After all, you are after this company many times richer than I do, because after the end I have as much money as I had in advance. I have not earned anything from this company on balance. My earnings are $0, while you have infinite money and may be causing a world crisis due to the huge inflation you will bring.

How can that be?

If, like me, when I heard this paradox for the first time, you do not know how I mysteriously did not get richer from this company, you are helping you to ask yourself the following.What numbers are on the dollar bills that are in my pocket at time [matht = 0 [/math?In other words, which dollar bills sit at time [matht = 0 [/math still in my pocket?

You will be wondering, perhaps to conclude that you cannot think of a number whose dollar bill is still in my pocket.After all, at the first time I give away dollar bill number 1, on the second number 2, on the third number 3, etc. So there is a time for each dollar bill that I give it to you. So I stay paradoxically, so with nothing about it!

This paradox works so well, because infinity passes our intuition.One simple solution is to make sure that we both become infinitely rich, is to not give you the dollar bills 1, 2, 3, etc. But to give you all the tenth notes and stop all the others in my own pocket. That is to say, I’ll give you number 10, 20, 30 etc. and stop 1 through 9 and 11t/M 19 and 21 through 29 etc. In my own pocket. This also goes against our intuition, because despite that I stop at a time as much in my own pocket as the last time it gets richer many times! How exactly everything works exactly, goes beyond this answer to explain.

If you are interested in more of this kind of paradoxes, then I recommend you to look up the paradox of the Hilbert hotel.

The Liars-paradox.

‘ I Lieg ‘

Does he speak the truth?

Your partner gets an accident and goes dead.

As a reaction, you build a time machine to prevent it.

But if it would succeed, your partner would never have died, so there was no reason to build the machine to prevent it

I always find this a nice one.Imagine you’ve bought a nice sports car. After a while you replace the wheels. Then the Windows. Some time later you replace some bodywork, the engine, gearbox etc. Until you have replaced each part in the car. Do you now have a new car, or is it still the old one (same car)? When did the ‘ switch ‘ took place?

Now IE comes real.All replaced parts have been stored in your garage. Now you use all the old parts to assemble an identical car. So now you have 2 cars that look exactly alike. Which is the original? When is the original stopped with the original. Or are they both original? Paradox芒 鈧?娄

A bad example is also a paradox.

This is the difference between the personal and the general.

For the convenience, I assume that reality around us is not an illusion, but really exists.

Yet we do not find the general important, only the personal counts.That my neighbor is dying of cancer is not bad, but that he runs to scream of pain so that I can not sleep that is only very.

We know that only the general is important, but we only count on the personal.This is the paradox.

Maybe you don’t think it’s a paradox, that’s a paradox.A paradox that is like a piece of paper around the real paradox.

What you think of this does not really interest me at all, but upvotes I find a kick, to describe the same paradox in other words yet again.

This question is confusing because there are different forms of a paradox.In spoken language, the linguistic paradox is usually used. In that case it means:

A paradox is an apparent contradiction.

A paradox consists of a combination of things that cannot at first glance, but which, if you think again, is indeed possible.

Favorite Example:

Writing is deleted.

Another example:

The more specialised someone is, the less he can.

God is almighty.

So he can make a stone that is so heavy that even he cannot lift him.

So he is not almighty.

The usual definition of a paradox is an apparent contradiction between two or more statements, which in themselves are true, but in combination lead to an infinite regression.

  • The following sentence is true
  • The previous sentence is not true

Or:

  • This is a good example of a paradox: this is not a paradox.

The paradoxical nature of statements, follows: A ruling about something, is not the same as what you are about.In other words: “ceci n’est pas pas un pomme“.Or-in terms of mathematics-a collection of elements is not an element. Or, in other words, on the word “chair” you can not sit.

Humanity is still in a phase of denial and thinks that paradoxes should be eliminated.The social pressure to conform to this is particularly important. What emerges from this paradoxical statement, which does not appear to be a paradox:

  • Brexit means Brexit

(for breaking a relationship, you need a relationship.I’ll call this a “Hotel California paradox:”you can check-out any time, but you can never leave“).

As is clear from the situation in the EU and GB: This leads to an eternal regression.Perhaps for the sake of completeness: The paradox does not continue to solve the EU too! As the Americans say: “damned if you do, damned if you don’t“.


Russell and Whitehead attempted to circumvent paradoxes by distinguishing between a ruling (“This is an apple“) and statements about statements (“This is a statement:” This is an apple“), the so-called” different “logical Types “.

Unfortunately, G枚del came up with an unrebuttal proof, that this also either creates an inner contradiction or an incomplete system (there are true statements, but they are not proving).

In Laws of Form , Spencer Brown demonstrates that the axiom “make a distinction” is sufficient to distract the whole logic and mathematics, including the phenomenon of the paradox.


I myself have gained the insight that this universe is inherently paradoxical. This followed from the evidence that you can only prove our existence from the fact that we exist.(Do not tell). A paradox goes beyond a ruling. Even without language, the universe consists of paradoxes.

The “Infinite Regression” shows itself as “infinite progression”, which we call “evolution”.From a paradoxical perspective I do not need any explanation or theory for evolution. This is how it works naturally. This is only necessary when you want to exclude paradoxes.

The paradoxical tensions are expressing themselves as energy.Paradox and energy are equivalent, equivalent. You cannot distinguish between a paradox and energy. (Between paradoxes among themselves). With every paradox, an energy is associated. Because energy is retained, paradox is also retained.

(Funny story in this regard.One of my fellow physicists-who disagree with my understanding-came up with this evidence for his point of view: “Energy can measure you. Paradoxes cannot be measured, so energy exists and paradoxes are not “.

To which I said: “Keep watch: I have said that energy and paradox are equivalent: You can measure the paradox by measuring the energy”.

You will also understand why tensions are rising (in families, between Alloch and natives, remain and Brexit, Democrats and Republicans, democracy and autocracy, poor and rich,…) As long as you continue to deny that the situation is inherently paradoxical. )

“A barber had a signboard that said,” I shave all men who do not shave themselves. “

A clever passer-by saw that, and asked the hairdresser: ‘ Who are you shaved? ‘

If he does not shy himself, he would do that according to the signboard.

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