Infinity (1 Viewer)

[SeDaTeD]

Actually, there is the same number (or cardinality) for both sets, as you can form a one to one correspondence between the two sets. Google up stuff on aleph-null.

 

[Raginsheep]

Actually, there is the same number (or cardinality) for both sets, as you can form a one to one correspondence between the two sets. Google up stuff on aleph-null.

Ah kool, one week of maths and I can understand that.....

 

[Riviet]

What about infinity in relation to indeterminant expressions? Which limits are indeterminant, instead of undefined?

 

[Templar]

How many numbers lie between 0 and 1? Infinite.
How many numbers lie between 0 and 2? Infinite.

How many what numbers? Rationals or reals? If both are rational then the cardinality is the same, if one is real and the other rational, the reals is a greater set than the rationals, even though both are infinite.

Actually, there is the same number (or cardinality) for both sets, as you can form a one to one correspondence between the two sets. Google up stuff on aleph-null.

I'd recommend Hilbert's Hotel.

Aleph one while you're at it.

And continuum hypothesis and axiom of choice and Gödel and...

 

[XcarvengerX]

How many what numbers? Rationals or reals? If both are rational then the cardinality is the same, if one is real and the other rational, the reals is a greater set than the rationals, even though both are infinite.



I'd recommend Hilbert's Hotel.

Aleph one while you're at it.

And continuum hypothesis and axiom of choice and Gödel and...

Honestly, I don't understand what you were saying. If you don't mind, can you tell me what is cardinality, Hilbert's Hotel, Aleph one, continuum hypothesis, axiom of choice and Gödel? Or at least give me some overview about each one... Thanks.

 

[Templar]

The number of rational numbers between 0 and 1 is the same as the number of rational numbers between 0 and 2 ie they have the same cardinality, for which we define as aleph null, the smallest set of infinity.

The number of real numbers has the same cardinality as well. So does the number of rational numbers between any two real numbers.

Hilbert used the Hilbert Hotel example to show that infinity and 2*infinity had the same cardinality.

The set of real numbers, however, is greater than the set of rationals. This is proved by Cantor using Cantor's diagonal method.

Worry about aleph one after you have fully grasped the concepts of aleph null.

The continuum hypothesis, axiom of choice, Gödel, Cohen etc are related to the foundations of maths. It was just a tongue in cheek remark to SeDaTeD. You do not need to worry about it. As a matter of fact, neither does he, because to go into detail about logic, consistency and undecidability is way too complex.

 

[Raginsheep]

I recommend wikipedia. Im not too sure about the others but cardinality refers to the number of elements in a set.
ie:there are 10 elements (1,2,3,4...10) in the set of integers between 0 and 10.

 

[darkliight]

I recommend wikipedia. Im not too sure about the others but cardinality refers to the number of elements in a set.
ie:there are 10 elements (1,2,3,4...10) in the set of integers between 0 and 10.

I say there are 9 elements
/nitpick

 

[Raginsheep]

err........yeah

 

[live.fast]

hey, if infinity is an abstract concept, den are diz true:
infinity > infinity + 1

how do u noe if infinity is an extremely large number, an endless unbound number (continuation of numbers) , a neverending always growing number, a set but 'infinite' number...wat da hell...and once u noe dat, den i guess u can tell me whether

infinity > inifinity + 1

 

[STx]

i dont think you can say 'infinity > inifinity + 1', but that inifinity + 1= infinity

 

[Templar]

hey, if infinity is an abstract concept, den are diz true:
infinity > infinity + 1

how do u noe if infinity is an extremely large number, an endless unbound number (continuation of numbers) , a neverending always growing number, a set but 'infinite' number...wat da hell...and once u noe dat, den i guess u can tell me whether

infinity > inifinity + 1

Once you have learnt how to spell and use proper grammar, then you can post your concerns.

 

[live.fast]

Wats me gramma n spellin got 2 do wif me qs? just coz sum of us aint all prim n prudish, aint mean u gotta dis me posts, alrite?

 

[live.fast]

oh n STx, y cant i say infinity > infinity + 1?

 

[Templar]

Poor spelling, grammar and lack of punctuations makes reading the posts difficult on an already difficult topic.

The best example to highlight infinity + 1 = infinity would be to use Hilbert's Hotel example. In addition Cantor's work into infinite sets also highlight peculiar properties of infinity, both of which you can read up if interested.

 

[pLuvia]

Infinity is not defined as a number, just something really big so you can't do normal additions, subtractions etc to it

 

[live.fast]

i'm lost =(

 

[onebytwo]

if infinity > infinity + 1
then, infinity - infinity > infinity - infinity + 1
then 0 > 1
which we all know to be absolutely ludicrous

 

[live.fast]

but if infinity is somesuper majorly massive number then,
wouldn't a supery majorly massive number be + 1 > then a superly majorly massive number?
or does the infinity 'eat' the 1 up? =) (i got a weird imagination..)

and onebytwo, you're treating infinity like a set number, but if it's infinity, then wouldnt you (and me come to think of it) be wrong? because doesn't infinity go on for like...infinity? =)

so i guess it comes down to,

what's the actual mathematical definition for infinity? Do you have to treat it differently for different cases? Is it an ever increasing number? Or is it, like some other dude said, just another way of saying 'big number'?

 

[pLuvia]

As I said before, infinity is not defined as a definate number, in your example you're treating it as a definate number.