Quote (ClarkeKent @ May 21 2010 06:19am)
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 the real numbers, the intervals (0,1) and (0, 2) are the exact same size. In fact they are the same size as the entire set of real numbers itself.
Common sense actually says that .999... does equal 1 O_O How much common sense does it take to answer this question: what number (or numbers) is between .999... and 1?