David Taylor wrote:
On 2006-10-20, The Natural Philosopher wrote:
Mike G wrote:
"The Natural Philosopher" wrote in message
...
Guy King wrote:
Nonsense. You can multiply infinity by anything you like (apart from
zero, of course), it just comes out as infinity again. Just a bigger
infinity.

You can multiply it by zero as well.
Yeah, but what would be the point in doing that?
All that calculation for nothing. :-)
Not at all. Infinity times zero can be any number.

Consider: 3/0=infinity.
now (3/0) * 0 is obviously 3, because the zeros cancel out...;-)

Actually no, 3/0 is undefined, and I'm not certain what the
result of (undefined * 0) is. It's probably still undefined
or possibly 0.

But infinity * 0 is still 0, I'm fairly sure.

Not really. Firstly, there was a smiley.

Secondly the sort of sum shown there is in fact the sort of sum that
lies at the heart of the 'calculus of infinitesimals..'

Where you want to calculate the value of e.g Dx/Dy as BOTH tend towards
zero.

Ultimately the tangent o a curve is definable as 0 divided by 0, but it
has a definite value all right...in the limit one says that it 'tends
towards a given value as dx and dy tend towards zero..obviously AT zero
the line is not a line - its a point and there can not be a tangent..but
the maths really says that you can make it as small as you want and it
will get closer and closer to a given value, as long as you never make
it infinitely small..
Except in discontinuous functions that have a divide by zero in them
anyway..like e.g. cotan(theta)..then not only is the function +-
infinity, but so its its derivative, at 0 degrees