Your Paradox.

[Contun]

What happens when you drop unbuttered toast?

Then you merely drop toast...?

 

[Soxafloppin]

What happens when you drop unbuttered toast?

Then you merely drop toast...?

Close, but no cigar.

You see theres no butter side for it to land on.

And we all know that toast allways lands butter side down.

My theory is that it would simply float above the ground, until it eventually comes into contact with butter.

 

[Contun]

What happens when you drop unbuttered toast?

Then you merely drop toast...?

Close, but no cigar.

You see theres no butter side for it to land on.

And we all know that toast allways lands butter side down.

My theory is that it would simply float above the ground, until it eventually comes into contact with butter.

... I just tested your theory, sadly, it was false... It burned a hole straight through my kitchen floor... Unhappy Face.

 

[The Unworthy Gentleman]

What happens when you drop unbuttered toast?

Then you merely drop toast...?

Close, but no cigar.

You see theres no butter side for it to land on.

And we all know that toast allways lands butter side down.

My theory is that it would simply float above the ground, until it eventually comes into contact with butter.

Sorry but toast only lands butter side down due to the height at which it is held for it to be dropped. if you hold it at twice the height then (theoretically) it should fall butter side up, meaning that toast does not always land butter side down. first guy was right, you just dropped toast, nothing spectacular.

*cracks knuckles* If a man who stated everything he has said and will say is a lie, is he telling the truth? (apologies if it's already been said, I just jumped in here)

 

[Maze1125]

With that sort of simplification, you can say an expression "works out to about three, give or take six billion" and still be accurate.

But that's the thing, you can't.

Infinity/infinity can be anything, including infinity itself.
So:
Infinity/infinity[sup]2[/sup] = (infinity/infinity)x(1/infinity).
Infinity/infinity could be infinity, which gives:
Infinity x(1/infinity) = infinity/infinity.
Infinity/infinity could be infinity, which gives:
Infinity

So, infinity/infinity[sup]2[/sup] could well be infinity as well. Without a rigorous derivation of the infinities in question, there is no way to tell.

There are a finite number of stars within a finite distance of Earth, but an infinite number that are infinitely far away. So it's actually inf[sup]2[/sup]/inf, which means the average distance is still infinite.

No, there aren't any stars an infinite distance away.
And, even if there could be, they wouldn't matter. What matters is that there are an infinite number of stars a finite distance away.

 

[TheSeventhLoneWolf]

Just State a Paradox to see how well we can understand one.

(The purpose of this thread is too see if a Paradox is actually possible)

I'll start one with the good old Futurama one where Fry ends up doing his own grandmother when time traveling in the past causing him to become his own grandfather.

That's not a paradox though. A paradox is something impossible which will fuck up the universe. Like if I went back in time to kill Hitler at birth then, in the future I'd have no reason to go back in time.

There's actually a game about that. Command and Conquer: Red Alert.

Spoiler: What happens in a nutshell

Einstien goes back in time and makes hitler vanish, russia never faced off in WW2 and became stronger, eventually attacking the west. The entire thing messes up though.

 

[Veret]

Aaaahh...headache...

With that sort of simplification, you can say an expression "works out to about three, give or take six billion" and still be accurate.

But that's the thing, you can't.

Spoiler: proof

Infinity/infinity can be anything, including infinity itself.
So:
Infinity/infinity[sup]2[/sup] = (infinity/infinity)x(1/infinity).
Infinity/infinity could be infinity, which gives:
Infinity x(1/infinity) = infinity/infinity.
Infinity/infinity could be infinity, which gives:
Infinity

So, infinity/infinity[sup]2[/sup] could well be infinity as well. Without a rigorous derivation of the infinities in question, there is no way to tell.

That's exactly right. inf/inf can only equal infinity if someone was lazy in setting up the original expression and said that the numerator was infinity, when it's really something like inf[sup]2[/sup] or higher. You can do that when speaking conceptually (infinity times infinity is still infinitely large), but you can't attempt any algebra with it.

So let's, as you said, rigorously derive the infinities in question.[footnote]This, by the way, is a really fun phrase. Props to you.[/footnote] This started with the assumption of an infinite universe, so set up the necessary equations, take the limit as r (radius of the universe) approaches infinity, and you'll see what I mean. I'd do it here, but this post is long enough and I am not going to attempt a calculus proof using forum BBcode.

There are a finite number of stars within a finite distance of Earth, but an infinite number that are infinitely far away. So it's actually inf[sup]2[/sup]/inf, which means the average distance is still infinite.

No, there aren't any stars an infinite distance away.
And, even if there could be, they wouldn't matter. What matters is that there are an infinite number of stars a finite distance away.

Nope. I'll refute this in two ways. First, the finite stars: Pick a finite radius; make it however large you like, so long as it's not infinite. Next, find the volume of that area (V = pi * r[sup]3[/sup]). Then find the number of stars in that area (V / v, where v is the volume of empty space around each star. Again, pick anything you like, so long as it's not zero). If the answer you got is infinity, then you're doing it wrong.

Now for the infinite stars. Let's just look at what's going on at the far "edge" of this infinite universe. We are imagining it to be a sphere for the purposes of this problem, so we need to find the surface area in order to calculate the number of stars it can hold. That's (4/3) * pi * r[sup]2[/sup], where r is infinity, so it's roughly inf[sup]2[/sup].[footnote]If we wanted to be exact, we'd keep the coefficients. But I don't, so I didn't.[/footnote] Given this infinite surface area, we can plop down a star every couple parsecs (or whatever finite distance you like), and it will hold an infinite number of stars. And that's just the outer edge; we can repeat the process with an infinite number of smaller rings (r = inf - 1, r = inf-2, etc) and still get infinite stars, all of which are infinitely far away.

 

[Maze1125]

Aaaahh...headache...

With that sort of simplification, you can say an expression "works out to about three, give or take six billion" and still be accurate.

But that's the thing, you can't.

Spoiler: proof

Infinity/infinity can be anything, including infinity itself.
So:
Infinity/infinity[sup]2[/sup] = (infinity/infinity)x(1/infinity).
Infinity/infinity could be infinity, which gives:
Infinity x(1/infinity) = infinity/infinity.
Infinity/infinity could be infinity, which gives:
Infinity

So, infinity/infinity[sup]2[/sup] could well be infinity as well. Without a rigorous derivation of the infinities in question, there is no way to tell.

That's exactly right. inf/inf can only equal infinity if someone was lazy in setting up the original expression and said that the numerator was infinity, when it's really something like inf[sup]2[/sup] or higher. You can do that when speaking conceptually (infinity times infinity is still infinitely large), but you can't attempt any algebra with it.

So let's, as you said, rigorously derive the infinities in question. This started with the assumption of an infinite universe, so set up the necessary equations, take the limit as r (radius of the universe) approaches infinity, and you'll see what I mean. I'd do it here, but this post is long enough and I am not going to attempt a calculus proof using forum BBcode.

Okay.
Let the let the light intensity reaching Earth from each star be a/(r[sup]2[/sup]) where a is a constant.
Let the star density, or stars per meter cubed, be d, which is a constant.

Then, for any given radius of the universe, the light reaching Earth will be:
light intensity x star density x volume of the universe
=
(a/r[sup]2[/sup]) x d x (4pi/3 r[sup]3[/sup]) = 4/3 (d pi r)
Let the radius of the universe (r) tend to infinity and the equation becomes infinite.

In fact, that is an underestimation, as it assumes that the light intensity of all stars would decrease as the universe has a large radius, when in fact only the "new" stars would have the reduced intensity.

So, even this gross underestimation, due to using simple multiplication rather than integration, still gives an infinite value for the light reaching Earth, assuming the universe is static and infinite.

There are a finite number of stars within a finite distance of Earth, but an infinite number that are infinitely far away. So it's actually inf[sup]2[/sup]/inf, which means the average distance is still infinite.

No, there aren't any stars an infinite distance away.
And, even if there could be, they wouldn't matter. What matters is that there are an infinite number of stars a finite distance away.

Nope. I'll refute this in two ways. First, the finite stars: Pick a finite radius; make it however large you like, so long as it's not infinite. Next, find the volume of that area (V = pi * r[sup]3[/sup]). Then find the number of stars in that area (V / v, where v is the volume of empty space around each star. Again, pick anything you like, so long as it's not zero). If the answer you got is infinity, then you're doing it wrong.

Now for the infinite stars. Let's just look at what's going on at the far "edge" of this infinite universe. We are imagining it to be a sphere for the purposes of this problem, so we need to find the surface area in order to calculate the number of stars it can hold. That's (4/3) * pi * r[sup]2[/sup], where r is infinity, so it's roughly inf[sup]2[/sup]. Given this infinite surface area, we can plop down a star every couple parsecs (or whatever finite distance you like), and it will hold an infinite number of stars. And that's just the outer edge; we can repeat the process with an infinite number of smaller rings (r = inf - 1, r = inf-2, etc) and still get infinite stars, all of which are infinitely far away.

Take the natural numbers.
If you go from 0 to any finite number , there will be finite natural numbers between 0 and n and each one will be a finite distance from 0.

For example n=3, we have both 1 and 2 in between 0 and 3, 1 is a distance of 1 away from 0 and 2 is a distance of 2 away from 0.

But, if you look at all natural numbers between 0 and infinity, then you get an infinite number of natural numbers, but they are all still only a finite distance away from zero.

There are infinite natural numbers, in an infinite space, but each one is only a finite distance from any other.

This is the same as stars in the universe.
You've shown that to have an infinite number of stars, you need an infinite amount of space, but you have not shown that those stars within the space must be infinitely far apart.

 

[FolkLikePanda]

I am my own father... through sex *****!

 

[Housebroken Lunatic]

Can the almighty God create a rock which he cannot lift?

God's will is what determines reality. If he wanted it to be unliftable, it would be. If he wanted to be able to lift it, he could. God controls the very nature of the universe, a rock once unliftable doesn't have to remain unliftable.
So the short answer is yes.

That answer doesn't work according to logic, because the state of the object in question would immediately change from "unliftable" to "liftable" the split-second God decides to lift the object in question. So God will inevitably fail in that regard, regardless of how many alternativ realities, timelines, gravity phenomena or fundamental changes to reality that the god in question might be able to have powers over.

Then again, "God" failing in logic isn't something particularly new.

(note: im not trying to invalidate christian faith or any other faith by illustrating why the proposed powers God is said to possess will fail according to logic. Everybody's got their reason to have faith in anything, and if it's something that makes it easier for people to get out of bed every morning then it's a perfectly reasonable thing to possess)



PS. Chuck Norris might however be able to pull off the feat in question XD

 

[RabidusUnus]

If a crocodile steals a child and promises its return if the father can correctly guess what the crocodile will do, how should the crocodile respond in the case that the father guesses that the child will not be returned?

It is opposite day today.

[It's gone]

I love that sophisme!
I have it in my paradox book which is not 1 meter away from me.


OT:
Suppose every man in a village is well shaven everyday.
A barber claims he shaves every man in the village who doesn't shave himself.
Question:who shaves the barber?

It may not seem like a paradox at first,but think about it a bit and imagine the possibilities.

Someone from out of town does it.