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[_r.u.s.s.]

we were talking about big numbers and then somebody mentioned infinity, we didn't have any rules about not discussing infinite sets=S

actually an infinite set is quite a biggie if you ask me

[Japo]

Yes yes I didn't call off topic, I'd be as guilty as anyone. :P But if we are discussing about all this at the same time we shouldn't confuse different concepts referred to with the same word.

BTW: http://en.wikipedia.org/wiki/Hilbert...he_Grand_Hotel

[DoomYoshi]

Originally Posted by _r.u.s.s.

try imagining it on dimensions. 1d line, 2d whole plane and brand new dimension, 3d next noncollinear vector and you've got another dimension with volume

Another way to imagine the differences between infinities is on a number line. The set of real numbers is infinitely larger than the set of integers for instance.

[dosraider]

This topic is filled with infinite LULZ.

[Bp103]

The concept of infinite is a loop, if I could see in a infinite view (if there was nothing blocking my view) i would see the back of my head.

That is how infinite was explained to me....

Infinite is NaN in real world and only expressible on paper and theory?

Lots of simple meaningless threads are becoming intellectual discussions here.

I love this place lots of smart people.:cheesy:


Anyways 9 is the biggest number, where all other Numbers are based on. *walks away with a headache*

[AlumiuN]

You wouldn't see the back of your head. To do that, your sight would not need to be infinite, but curved over the surface of the Earth. And the concept of infinity can not be proved or disproved in physical terms because the human mind has no capacity for comprehending an infinite distance or an infinite set of numbers or objects.

And yes, this place is overflowing with smart people. :thumbs:

[rlbell]

Originally Posted by DoomYoshi

I accidentaly figured out two different sized infinities. There are an infinite number of prime numbers. There are also an infinite amount of numbers which are not prime. However, at any given point after 10, the number of prime numbers will be smaller than the number of not prime numbers. Hence, a smaller infinity. Trippy, huh?

Actually, there are as many integers as there are primes. They are both countable sets. Between any two integers, or any two primes, there are only a finite number of elements. A bigger infinity is the set of real numbers. Not only is there an infinite number of them, but there is an infinite nmber of distinct real numbers between any two elements.

The bit with Achilles and the tortoise is that while there are an infinite number of slices of time with Achilles not cathing up to the tortoise, the sum of the durations of that infinite number of instances is a finite number. If the tortoise has a 100 meter head start and scampers at the un-tortoiselike speed of one meter per second to Achilles leisurely (for Achilles) ten meters per second, the total duration of all those instants of time one hundred nineths of a second, for a total distance of one nineth of a kilometer

[SlowCoder]

Originally Posted by rlbell

Actually, there are as many integers as there are primes. They are both countable sets. Between any two integers, or any two primes, there are only a finite number of elements. A bigger infinity is the set of real numbers. Not only is there an infinite number of them, but there is an infinite nmber of distinct real numbers between any two elements.

The bit with Achilles and the tortoise is that while there are an infinite number of slices of time with Achilles not cathing up to the tortoise, the sum of the durations of that infinite number of instances is a finite number. If the tortoise has a 100 meter head start and scampers at the un-tortoiselike speed of one meter per second to Achilles leisurely (for Achilles) ten meters per second, the total duration of all those instants of time one hundred nineths of a second, for a total distance of one nineth of a kilometer

Is there a smiley dictatiing an exploding head? Oh, well, let's have a go ... :boom:!

[arete]

Oh dear *goes crosseyed* ... I think I've just gone crosseyed...

[Kugerfang]

Infinity is not a number, it's a concept.