Originally posted by oddbobI don't understand. How is this showing that the albatross can count? It seems to me that the fisherman is doing the counting.
There is a type of albatros that is able to count. The fisherman will give the bird a fish for every 10th or so one it's caught.
We agree that the bird doesn't understand language as we do so
what represents numbers in its mind?
Emotions?
Originally posted by doublezClassical logic is insufficient for dealing with infinite sets.
whaddaya mean NOT?
obviously 3 is not a perfect square, already integers are one up...
Every integer can be put into one-to-one correspondence with a perfect square.
1 -> 1
2 -> 4
3 -> 9
etc.
Hence the two sets are said to have an equal number of members (same cardinality).
See
http://mathworld.wolfram.com/CountablyInfinite.html
http://mathworld.wolfram.com/Aleph-0.html
yes but you obviously haven't read any galileo.
read this: http://www.firstscience.com/site/articles/infinity1.asp
quite obviously, the set of perfect squares is a subset of the set of integers, and since it has been shown that some (ie most) integers are not in the set of perfect squares, the set of integers is larger, though they may both be infinite.
Nice try simplicio!
Originally posted by doublezBecause an infinite set is a proper subset of another infinite set does not necessarily imply that the latter is larger.
yes but you obviously haven't read any galileo.
read this: http://www.firstscience.com/site/articles/infinity1.asp
quite obviously, the set of perfect squares is a subset of the set of integers, and since it has been shown that some ...[text shortened]... s larger, though they may both be infinite.
Nice try simplicio!
How do you define the 'largeness' of an infinite set?
Read Cantor, not Galileo!
From your own source: You can effectively have 'smaller' and 'bigger' infinities, one a subset of the other, that are nonetheless the same size.
You can take a horse to water but you cannot make it THINK!
from the quote you gave (from my source) it implies that when one infinity is a subset of another it is smaller.
Also, about two sentences earlier it is stated:
"But here's the rub. There are lots of numbers that aren't squares of anything. So though there's a square for every single integer - an infinite set of them - there are even more individual numbers than there are squares."
So i win.
Originally posted by doublezYou haven't a clue what you are talking about.
So i win.
In future you should stick to finite sets, sonny.
Originally posted by doublez
from the quote you gave (from my source) it implies that when one infinity is a subset of another it is smaller.
It said 'smaller', not smaller. Notice the difference? Duh.
Originally posted by doublez
Also, about two sentences earlier it is stated:
"But here's the rub. There are lots of numbers that aren't squares of anything. So though there's a square for every single integer - an infinite set of them - there are even more individual numbers than there are squares."
Infinity + Infinity = Infinity
or, more precisely,
Aleph(zero) + Aleph(zero) = Aleph(zero)