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☖ Forums → Discussion Forum → Which is bigger?
Which is bigger?
2007-03-10, 11:47 AM #1
I don't think we have enough blow-your-mind polls going on these days. So:

Take the total number of integers (infinite), and the total number of real numbers between 0 and 1 (also infinite). Which set is larger?
Stuff
2007-03-10, 11:48 AM #2
Mine's bigger than yours wee man.
Code:
if(getThingFlags(source) & 0x8){
  do her}
elseif(getThingFlags(source) & 0x4){
  do other babe}
else{
  do a dude}
2007-03-10, 11:50 AM #3
Im not that good at Maths, but I work it out if I could get my brain in gear :)
Its the weekend - brain turns off :)
2007-03-10, 11:50 AM #4
They are incomparable, obviously.
For row of integers, there will be always a number more/less then any picked one.
For row of reals, there will be always a number inbetween any two picked out on this range, no matter, how close.
I don`t suffer from the lack of sanity.
It`s others, who have it in excess.
2007-03-10, 12:20 PM #5
Reals are uncountable, integers are countably infinite. Thus the set of reals from 0-1, or any set of reals for that matter, is "bigger" than the set of integers. Thank you, Cantor.
2007-03-10, 12:22 PM #6
I still say, that comparing infinite numbers is iffy.

If both could be presented as series... But it`s clearly impossible for the real numbers between 0 and 1.



However... For each natural N, there is one 0.N in reals, and -N and +N in integers. Therefore, integers are twice as big...?

As I said, it`s impossible to compare both like this.
I don`t suffer from the lack of sanity.
It`s others, who have it in excess.
2007-03-10, 12:26 PM #7
Which is bigger though set of all natural numbers 0 and greater or the set of all numbers positive and negative?
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2007-03-10, 12:29 PM #8
Originally posted by Alice Shade:
However... For each natural N, there is one 0.N in reals, and -N and +N in integers. Therefore, integers are twice as big...?

As I said, it`s impossible to compare both like this.


Actually, using cardinality as a judge of size, they're both equal because they have the same cardinality (both countably infinite).
2007-03-10, 12:32 PM #9
That`s exactly it. Both are infinite... And yet, as I showed, integer infinity contains twice as much numbers.

Mindbreak, anyone?
I don`t suffer from the lack of sanity.
It`s others, who have it in excess.
2007-03-10, 1:21 PM #10
The reals between 2 and 3 is bigger than between 0 and 1
:master::master::master:
2007-03-11, 12:30 AM #11
Ow ow ow ow ow ow ow.
error; function{getsig} returns 'null'
2007-03-11, 9:34 AM #12
Set of all real numbers between 0-1 is smaller because it never exceeds 1.
"Jayne, this is something the Captain has to do for himself"

"N-No it's not!"

"Oh."
2007-03-11, 11:14 AM #13
Value of elements in a set has no bearing on the cardinality of a set.
2007-03-11, 12:24 PM #14
Originally posted by Alice Shade:
That`s exactly it. Both are infinite... And yet, as I showed, integer infinity contains twice as much numbers.

Mindbreak, anyone?


I thought we already established that you don't understand mathematics in any form?

:saddowns:
2007-03-11, 1:11 PM #15
Originally posted by Darth:
Reals are uncountable, integers are countably infinite. Thus the set of reals from 0-1, or any set of reals for that matter, is "bigger" than the set of integers. Thank you, Cantor.

This man speaks the truth.
[This message has been edited. Deal with it.]

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