Paranormal Events

I hope that's sarcasm because my head doesn't quite see how "infinite < infinite" makes sense

For two infinite sequences too be equal there must be some mapping that for all x in 1 set you can arrive at all x in the other. This is obviously possible for Natural numbers to Integers but there exisits no mapping from Integers to Reals. There are infintely many numbers in the integers (...,-3,-2,-1,0,1,2,3,...) take any sub interval on this in the reals say (0,1) then there are infintely many numbers between those two numbers, since there are infintely many sub intervals in the intergers then the reals are infintely many more numbers in the reals than there are in the integers. However take any sub interval in the reals, this has the same size as the whole set of reals which is mad right? but its about a mapping. for instance tan(x) for (\( \frac{-\pi}{2},\frac{\pi}{2} \)) takes every point in this interval to every number in the reals. Which is why the concept of infinty is to me paranormal.

But about ghosts, i dont believe and wont believe without good evidence of which there is none atm.
Life outside of our own planet, yes i think so.
Intelligent life outside our own planet, yes i think so.
 
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There are infintely many numbers in the integers (...,-3,-2,-1,0,1,2,3,...) take any sub interval on this in the reals say (0,1) then there are infintely many numbers between those two numbers, since there are infintely many sub intervals in the intergers then the reals are infintely many more numbers in the reals than there are in the integers..

This argument isn't valid. There are infinitely many numbers in the interval (0,1) if we're working in the rationals. However, the rationals are countably infinite (mapping p/q (in lowest terms) to (2^p)*(3^q) works).
 
What do you guys think of Randi?

I love what the JREF do. (Also if anyone doesn't already, I highly recommend listening to the Skeptics Guide to the Universe... I went through all 350 episodes in about 4 months, and learned sooooooo much about all these pseudosciences).
The infinity and evolution things seem like they should be threads in their own right.
Anyway, this thread is great, I'm just going to go and get some more popcorn :)
 
What if I told you there were as many integers (ie ... -2, -1, 0, 1, 2 ...) as there are natural numbers (ie 0, 1, 2 ...)?
Makes sense I'd say..? My head agrees with this.

In short: mathematicians distinguish different infinities, two infinite sets being the same "size" if you can pair up their elements. For example integers (on the left) and natural numbers (on the right):

0 <-> 0
1 <-> 1
-1 <-> 2
2 <-> 3
-2 <-> 4
3 <-> 5
-3 <-> 6
...

That's a simple rule to match all integers with all natural numbers, so they're considered the same size. You can't do that with natural numbers and real numbers, so in this sense there are more real numbers than natural numbers.
I think I understand, thanks for clearing that up. but does this hold significance in the real world or is it just for the sake of math? I'd guess that it does have some use but I'm struggling to think of any examples.


Well, maybe they're right. Can you show the example that caused you to ask this?
It was more of a general comment as how arguments usually start to stray from the original point because people just like arguing/debating so much. If you really like, I could find an example of this but I fear that this is drifting off-topic. Maybe I should say "I like ghosts" just to make this a little more relevant.

I should probably stop saying it because it confuses people sometimes.

Or try "not even a debatable issue" or something? Stock phrases are cool, don't bin them, just tweak them. :)

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Also on a very very side note:
...then answer Zinc's perfectly legitimate question appropriately.
I agree with Zinc
Not that this has any significance, but I'm ZincK, the nickname wasn't intended to be related to the metal and was a rather annoying coincidence ("Zinc Potassium? what does that mean?"). You have no idea how happy it would make me if you called me ZincK (and I had no idea how creepy that would sound until I typed it).
 
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Life outside of our own planet, yes i think so.

Able to traverse the galaxy (science alien) I have trouble believing.




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Personne ne maîtrise parfaitement un 2x2, alors imagine les autres.
 
This argument isn't valid. There are infinitely many numbers in the interval (0,1) if we're working in the rationals. However, the rationals are countably infinite (mapping p/q (in lowest terms) to (2^p)*(3^q) works).

I dont see how your point is any more valid since i was talking about the reals and youve taken a sub set of that which was countably infinite and ingnore almost every number there is in due to the irrationals being uncountably infinite. I was using it as a thought experiment not a proof (obviously), if you can show 1 interval contains infinite numbers in one number system and a finite number in another yet there are infinitely many of those intervals in the set then the two sets cant be equal size i.e. the cardinality ("size")of \( \mathbb{R} \) is not equal to the cardinality of \( \mathbb{Z} \) even though they are both infinite sets.
 
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You're argument effectively boiled down to that in the reals there are infinitely many sub-intervals each containing infinitely many numbers, so there must be more reals than natural numbers. I was saying you could also apply the same logic to the rational numbers (that is, in each interval of length one, there are infinitely many numbers, and there are are infinitely many such sets) yet you still have a countably infinite set.
 
E=mc^2

That says you need a infinite amount of energy to accelerate anything that has a mass to the speed of light. So you have to go at least a bit slower than light. The nerest star is approx 4 light years away, so if they comes from there they need to travel more than four years to get here.

But, that is if you can reach that speed in no time, but if you did the G-forces would make you look like a pizza, flat and messy. You need to accelerate slowly, for humans not more than 1.5-2 G is possible in longer periods.

Get it, no aliens comes here because it would take too long to travel! (for the same reasons humans will never leave this solar system).

An argument is: "but they use stargates, wormholes, whatever..."

And things like that exists outside sci-fi?
 
E=mc^2

That says you need a infinite amount of energy to accelerate anything that has a mass to the speed of light.
Nope, wrong formula. This one says that you can convert between energy and mass, with a conversion factor of c^2.

So you have to go at least a bit slower than light.
To be fair about this, current theory only says that you can't go faster than the speed of light relative to local space. Technically, it would be possible to travel a distance faster than light by somehow finding a shorter path (such as a wormhole). We just don't know enough about the possibilities to anticipate what kind of technology an alien race might use.

You need to accelerate slowly, for humans not more than 1.5-2 G is possible in longer periods.
Actually, "With a G-suit, accelerations of up to 8G can be tolerated for relatively long periods of time" - although it'd still take over a month, which I guess isn't THAT bad. And perhaps a spaceship designed for near-light speed would have even better technology than this, so very high accelerations would be no problem.

An argument is: "but they use stargates, wormholes, whatever..."

And things like that exists outside sci-fi?
Who knows? We still propel our ships through space by shooting stuff out one end. I think humans have a very long way to go before space travel is remotely practical, and before we can even decide what's possible and what isn't.
 
That says you need a infinite amount of energy to accelerate anything that has a mass to the speed of light. So you have to go at least a bit slower than light. The nerest star is approx 4 light years away, so if they comes from there they need to travel more than four years to get here.

You have forgotten or don't know to take into account that time slows down as you approach the speed of light. You could potentially get up to high enough speeds that you could travel lightyears per second (by your watch but for a stationary object your trip would take years).
 
You have forgotten or don't know to take into account that time slows down as you approach the speed of light. You could potentially get up to high enough speeds that you could travel lightyears per second (by your watch but for a stationary object your trip would take years).

Gravity also speeds up time, I don't now how much time it is in empty space whith no greate mass nearby?

You travel for a few years, but at home hundreds of years passes, it will be much like a trip with no return...
 
You got that flipped turnways.

Eh? I did not get that because your expression is new to me (I'm not a native speaker) And I was asking because I don't know...

So? Doesn't mean we can't do it.

What I'm trying to say is that it takes much too long time, and here we are talking about the nearest stars, how big is the chance aliens dwells there, most stars are much more distant.
 
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