Paradox (maybe) disproving almost everything

[LABHOUSE]

This may be in the wrong section.

If everything were impossible then it would be impossible for something to be impossible.

2 + 2 = 4 is true and so is the opposite; this is true for the above also. (it is possible for everything to be possible)

But then it proves itself wrong as it is possible for something (currently just one random anything) to be impossible. (Infinity - 1 things possible)

But it would also be impossible for (Infinity - 1) things to be possible. (Infinity - 2 things possible now)

See it could continue until zero things were possible then negative things would be possible.

It would then continue until (infinity - 1) things are impossible.

Edited November 20, 2014 by LABHOUSE

[N_las]

You have to give a definition of what you mean by "possible", "impossible", "something" and "everything".

Human language is incredibly imprecise. Many words have many different meanings based on context.

It is not useful to use imprecise words in a logical argument.

Feathers are light. light is not dark -> There are no dark feathers.

[Dkmdlb]

You can't subtract finite numbers from infinity and eventually get to zero.

[MockKnizzle]

Why are you assuming that everything is impossible? That's clearly not the case. Additionally, a statement being true does not imply that its opposite is also true. For example:

Every square is a rectangle. (true)

Every non-square is a non-rectangle. (false)

There really isn't anything logical about OP's "paradox".

[LABHOUSE]

You can't subtract finite numbers from infinity and eventually get to zero.

You can if you subtract the finite numbers indefinitely you would essentially be multiplying any finite number but zero by infinity then subtracting it once.

Edited November 21, 2014 by LABHOUSE

[m4ti140]

No, you can't... This is not how the concept of infinity works. If you subtract a finite number from infinity you get infinity. And you cannot subtract infinity (infinity * finite number is infinity) from infinity, because you get an indeterminate form - which is certainly not 0. That's right, one can prove mathematically that infinity - infinity is not 0 and that it's impossible to determine what it is.

Sorry but.... you broke the mathematics with your OP.

[Mazon Del]

Amusingly enough, within mechanical engineering in linkage design, you routinely deal with adding and subtracting infinities, which is a completely different situation that won't help OP here.

Example:

You have a fixed bar. It can not move or rotate. Everything about it is known. Zero infinities.

You now have a second bar that is attached to the first bar with a hinge. The first bar cannot move, but the second bar can rotate at the point where the corners meet. Because the second bar can rotate to any angle between its limits (0-360, 0-45, 0-90, 0-45.12341235, doesn't matter) you have a system with 1 infinity in it.

You now add a third bar to the system. One of its ends is hinged to the end of bar two. The other end is left free. The same conditions to bar 2 apply to bar 3. Bar 2 can rotate wherever it wants and is not mechanically forced by 3 to be at any given angle. 1 infinity. But bar 3 is also not being restricted by bar 2, it can be at any angle on its hinge. 1 infinity. 1 infinity + 1 infinity = 2 infinities.

You now take the free end of your third bar and you give its free end a hinge that connects to the free end of the first bar. Bar 2 cannot rotate because one end is stuck to an immovable object, the other end is can only move in a way that would stretch of crush bar 3, which it cannot do. 0 infinities. Bar 3 also exists with these conditions and thus cannot rotate. 0 infinities. 0 + 0 = 0 infinities.

There is a lot of math and formulas that go into trading infinites to make your system more predictable with less motors and actually being able to get the motion you want.

[ZetaX]

Mazon Del: that's not an infinity, but a degree of freedom. Something completely different.

[Mazon Del]

Well yes...thus my statement to that effect at the beginning.

[ZetaX]

Do engineers really call them "infinities"¿ Sounds like a completely weird naming scheme...

No, you can't... This is not how the concept of infinity works. If you subtract a finite number from infinity you get infinity. And you cannot subtract infinity (infinity * finite number is infinity) from infinity, because you get an indeterminate form - which is certainly not 0. That's right, one can prove mathematically that infinity - infinity is not 0 and that it's impossible to determine what it is.

Sorry but.... you broke the mathematics with your OP.

Note that there are several ways to turn "infinity" into a number (but normally, it should not be treated like a number at all, more like an exception akin to NaN), for example http://en.wikipedia.org/wiki/Surreal_number .

[TheDarkStar]

Why are you assuming that everything is impossible? That's clearly not the case. Additionally, a statement being true does not imply that its opposite is also true. For example:

Every square is a rectangle. (true)

Every non-square is a non-rectangle. (false)

There really isn't anything logical about OP's "paradox".

Actually, a statement's opposite is always true if the statement is always true; you just have to properly take the opposite. The opposite of your statement would be "No non-squares are not non-rectangles", which is true. The problem with the original statement is that infinity is not normally a number and can't always be treated as if it is.

Edited November 21, 2014 by TheDarkStar

[dansmithers]

The opposite of your statement would be "No non-squares are not non-rectangles", which is true.

No it isn't. via negation, that statement is equivalent to "No non-squares are rectangles".

[Aethon]

2+2 does not always equal 4. 2 liters of water added to to 2 liters of ethyl alcohol don't result in 4 liters of solution.

[ZetaX]

2+2 does not always equal 4. 2 liters of water added to to 2 liters of ethyl alcohol don't result in 4 liters of solution.

That's because "2" is something different than "2 litres of water". You can't neglect units.

[magnemoe]

That's because "2" is something different than "2 litres of water". You can't neglect units.

True, also chemistry and physic add more issues, stuff might take less volume or blow up if mixed.

[Mazon Del]

Do engineers really call them "infinities"¿ Sounds like a completely weird naming scheme...

In my classes they did, but it was basically used interchangeably with "degrees of freedom". Most people in those classes tended to use degrees of freedom because it sounds less ridiculous.

[cicatrix]

I wondered what would happen if I divided infinity by zero?

[Mazon Del]

You fool! That is how you build a kraken beacon!

[Guest]

you don't need infinity just divide anything by 0 and KRAKEN occurs

about OP I think the key is that there's different types of infinity, big, small, countable, uncountable. you can take Hilbert's paradox for example (KSP sauce):

Let's say the maximum part count is infinity, and you have built a huge rocket with infinite fuel tanks now it seems like you can't add anymore parts, but if you move all tanks up by 1 you will get a new spot for a tank at its bottom right? This is for adding finite to infinite.

Now you can move tank number 1 to location of tank 2, move tank 2 to location 4, move tank 3 to location 6, etc and you will be able to add another infinite amount of parts to your rocket without ever contradicting the maximum part count.

You can if you subtract the finite numbers indefinitely you would essentially be multiplying any finite number but zero by infinity then subtracting it once.

For this there's a simple equation (demonstration by absurd):

i'll use 8 for infinity

Your statement: 8-8 = 0

but as 8 + real number = 8 you can add 1 to both sides and get this:

8-8+1 = 1 <> 8-8 = 1

and then contradiction, it's impossible for infinity - infinity to be both equal to 0 and 1

or you can also use the property that 2*infinity = infinity and substitute it like so

8-8 = 0 <> 8-(8+8) = 0 and then use your initial statement again, 8-0 = 0 <> 8 = 0 ???

Edited November 21, 2014 by RevanCorana

[KerikBalm]

If everything were impossible then it would be impossible for something to be impossible.

Proof by contradiction:

Not everything is impossible.

2 + 2 = 4 is true and so is the opposite;

Ummm... what? what is the opposite of 2+2 = 4....

I don't even.... whaaat....... you list your location as your mind, but I'd say you are out of it

this is true for the above also. (it is possible for everything to be possible)

What is true for the above alse?

How did you get to it is possible for everything to be possible?

But then it proves itself wrong as it is possible for something (currently just one random anything) to be impossible.

What proves itself wrong?

Proof by contradiction:

Not everything is possible

(Infinity - 1 things possible)

But it would also be impossible for (Infinity - 1) things to be possible. (Infinity - 2 things possible now)

See it could continue until zero things were possible then negative things would be possible.

It would then continue until (infinity - 1) things are impossible.

Umm... yea... whatever

I think you need to learn the difference between the converse, and the contrapositive.

Suppose we have the true statement:

If P, then Q

It does not follow that:

If not P, then not Q

(The converse/negation of the statement)

But it does follow that:

If not Q, then not P

(the contrapositive of the statement)

[Guest]

I wondered what would happen if I divided infinity by zero?

Indeterminate expression, unless you're working with limits. In this case, you usually need some finagling to figure out what the expression actually tends to (it'll likely be something mundane, though). I've seen a proof of a theorem about derivatives that ended up with infinity by zero division at a point. You could then use another theorem to figure out what the whole shebang tended to (a natural logarithm, in case you were curious).