Ok, so on tonight's news they reveal that all this time we've actually been orbiting the moon and not the sun. Meh - it made no difference to my life thus far and it will have no further effect.x EvilErmine x said:
World's best suggested paradox
- Thread starter royohz
- Start date
Lolwut?x EvilErmine x said:
Theoretical mathematics is far far more precisely defined than the physical concept of distance.
0.999... only exists with-in the concept of mathematics anyway. If you want to forget that and just "deal with reality" or something like that, then the idea of being 99.999...% of the way across doesn't exist at all, and so is a meaningless thing to say.
Either you're all the way across, or you are a clear and precise distance away from being all the way across.
Another way of visualising dividing...The Seldom Seen Kid said:
How many of one thing can you fit into another?
Four divided by two is two, because you can fit two twos into four (and do a passable impression of an owl while you're at it).
How many zeros can you fit into something? As many as you like; they have no effect.
Two divided by zero is infinity, because an infinite number of zeros would go into two.
You'd still have two left over afterwards though, so the actual answer (and kind of a paradox in itself) to the sum two divided by two is
infinity... remainder two.
Not necessarily.M0PHEAD said:
0 x infinity isn't necessarily 0. It can, in fact, equal exactly 2, although not always. (0 x infinity can equal any number, including 0 and infinity themselves.
So, the answer to 2/0 is infinity exactly, with no need for a remainder because we can specify that it is the infinity that is such that infinity x 0 = 2.
And, before anyone mentions it, mathematically speaking, everything I said there was utterly imprecise, but it wasn't meant to be, I was going for an understandable explanation rather than mathematical precision.
God is Awesome (If he's real)
My Top Hat is Awesome.
God is everywhere at once.
My Top Hat is on my head, and is not anywhere else.
Mm.
My Top Hat is Awesome.
God is everywhere at once.
My Top Hat is on my head, and is not anywhere else.
Mm.
Hang on... you're saying that there's a hypothetical value which when multiplied by zero is equal to two? As I understood it, zero represents nothing- and however many nothings you have it still equates to nothing, right?Maze1125 said:
As a maths student I find what you're saying, if correct, pretty damn interesting; I don't suppose you've got a link to a page which explains it a bit more thoroughly?
Like I said, I was being imprecise.M0PHEAD said:
The precise way to do such a calculation would be through limits.
Consider the function f(x) = 2x/x.
For all non-zero values of x, f(x) = 2, but f(0) is undefined as it contains 0/0. What you can do is consider the function as 2/x * x which, at x = 0, would be equal to infinity * 0.
This still does not give an answer unless you assume that infinity * 0 has a precise answer, which we cannot do.
So, we need to consider the limit, but for all x =/= 0, f(x) = 2 so it is easy to deduce the limit of the function as x tends to 0 is also 2.
We still do not have justification for claiming f(0) = 2, but what we can do is define a new function g.
Where, for x =/= 0, g(x) = f(x) and g(0) = 2.
g is then a continuous and differentiable function that equals f everywhere except for x = 0 where f did not have a value and g equals 2.
The point at x = 0 is called a removable singularity [http://en.wikipedia.org/wiki/Removable_singularity].
Now, most of that was pretty much rambling for the sake of precision. The point is that, because we are considering the function 2x/x, we know both that, at x = 0, the function is equal to infinity * 0 but also that the function is equal to 2.
So, in this case, infinity * 0 = 2.
(That last paragraph was mildly imprecise again.)
So it's more an assumption for the sake of convenience, based on maintaining the pattern set by more easily quantifiable numbers? Imprecise by nature but also kind of awesome- and way less of a cop-out than having a remainder floating around like a... Thing that floats...Maze1125 said:
A duck!
Thanks for explaining
Alright, check this out.
Hypothesis: All Ravens are Black.
Contrapositive: All Non-Black things are Non-Ravens. {Let's say that you are God and can see that this is actually true.}
Empirical Evidence: There is a Red Herring (A Non-Black, Non-Raven). {This partially confirms the hypothesis, as does every other Non-Black, Non-Raven thing found in the world.}
Conclusion: The hypothesis is true.
Empirical Evidence: If the same Red Herring is used to prove that hypothesis, it can also be used as evidence of a Non-White, Non-Raven.
Hypothesis #2: All Ravens are White.
Contrapositive #2: All Non-White things are Non-Ravens.
-Refer to Evidence above-
Conclusion #2: Hypothesis #2 is also true.
Final Conclusion: Black is White. QED.
This is known as Hempel's paradox - it can be used to prove just basically anything.
Hypothesis: All Ravens are Black.
Contrapositive: All Non-Black things are Non-Ravens. {Let's say that you are God and can see that this is actually true.}
Empirical Evidence: There is a Red Herring (A Non-Black, Non-Raven). {This partially confirms the hypothesis, as does every other Non-Black, Non-Raven thing found in the world.}
Conclusion: The hypothesis is true.
Empirical Evidence: If the same Red Herring is used to prove that hypothesis, it can also be used as evidence of a Non-White, Non-Raven.
Hypothesis #2: All Ravens are White.
Contrapositive #2: All Non-White things are Non-Ravens.
-Refer to Evidence above-
Conclusion #2: Hypothesis #2 is also true.
Final Conclusion: Black is White. QED.
This is known as Hempel's paradox - it can be used to prove just basically anything.