h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

A point about infinity - infinity isn't a number, its the limit of an unending sequence. It's fairly easy to show that there are different 'sized' infinities as well. Consider the natural (counting) numbers. That is an infinite series: 1,2,3,4,5,.. but between any two natural numbers there are a *finite* quantity of numbers. (eg. between 4 and 8 there are 3 numbers - the same holds for *any* two natural numbers.)

Now consider the real numbers (ie. numbers with decimal places). Again it is an infinite series - for any real number, you can think of a bigger one. However, between any two real numbers, you can find an infinite quantity of real numbers. Between 1 and 2, for example, is 1.5; between 1 and 1.5 is 1.25; between 1 and 1.25 is 1.125 etc etc...

Hence, the limit of the series of real numbers is a larger infinity than the limit of the series of natural numbers.

Er... there may be a spurious argument there...

For every time you can add a fractional number between two numbers in the series of real numbers, you can equally well add another number on the end of the series of natural numbers. Both are "Aleph Null" infinities... You need something like "Cantor's Diagonal Slash" (not a urinary complaint!) to show a differing level of infinity...

thank you ,may have better understanding now as to why front main speakers sound so good at natural sound levels Qa