Quote (ClarkeKent @ May 21 2010 01:19am)
In cricket, there are 42 standard rules.
Anything that isn't covered by them is covered by the 43rd rule. Common sense.
Infinity is immeasurable.
But grab a ruler, look between 0 and 1cm.
How many numbers are there between them? Infinity
Next step is look between 1 and 2cm.
How many numbers are there between them? Infinity
Finally, looking between 0 and 2. We find that there is also infinity numbers between them.
Are each of these infinte numbers the same?
Using rule 43, common sense, of course they are not. 0-2 is bigger than 0-1.
Common sense also says that .99... does not equal 1, just the same as 99 does not equal 1.
In mathematics, there are 8 axioms. Anything not covered by the axioms is called unprovable and ignored. Thankfully, this result is covered by the axioms and the correct answer is not what you expect.