Why Is Australia Not Considered An Island ??

Why Is Australia Not Considered An Island ?? Dec 23, 2019 5:33:36 GMT

Quote

Post by Hairynosedwombat on Dec 23, 2019 5:33:36 GMT

Dec 23, 2019 4:14:11 GMT Jep Gambardella said:

Dec 23, 2019 2:30:37 GMT Hairynosedwombat said:

George Cantor might disagree with you here. You imply that there are more rectangles than squares.

We can map (or make a one-to-one correspondence) between each member of the set of all rectangles and the set of all natural numbers (ie 1, 2, 3...).

We can make the same mapping of all squares with the natural numbers.

Therefore I would suggest (and I believe Cantor proved) that the set of all rectangles and the set of all squares are the same size.

That is ridiculous. Obviously there are more rectangles than squares. Both numbers are infinite, but one is bigger than the other - just like the number of multiples of 3 is bigger than the numbers of multiples of 5 (even though both are infinite).

It is a long time since I learnt this stuff so I might not get the terminology correct.

I was wrong above. The set of squares or rectangles cannot be mapped to the natural numbers.

However they are all infinite sets so that the set of squares and rectangles are said to have the same cardinality or size.