Cedric,
As a follow up, when doing high precision arithmetic (in engineering, numerical integration, weather prediction and the like) you usually have a setup routine that does things like:
BEGIN let a = 0.5 let b = a /2.0 while ( (a+b) <> a ) do epsilon = b b = b/2 endwhile
then epsilon is close to machine epsilon.
More sophisticated algorithms give more accurate values.
from that point we do indeed use ABS(a - b) < epsilon for 'close enough to equal'. There are a huge number of arithmetic tricks used to try to keep the accumulated rounding errors within known bounds as well.
Some calculations are very badly behaved, and there is very little we can do to try to keep results even remotely close to accurate. Chaotic systems are one class of problems that comes to mind (found in weather prediction for example). Another is inverting certain matrices - the Vandemonde matrix is a classic example that is not singular, but you get numbers that are less than machine epsilon so you find yourself trying to divide by machine zero (or even worse get 0/0, known in computing as NaN , or NotANumber), even though it can be proved that these matrices do indeed possess inverses.
I hope this makes you aware of how nasty floats and doubles (and quad and decwords) are in computer arithmetic. One book worth reading for a (relatively) gentle introduction to this is "An Introduction to Numerical Computations" by Yakowitz and Szidarovszky. A more exhaustive treatment can be found in "The Art of Computer Programming" by Donald Knuth, but that is not a read for the light hearted. "Programming Pearls" by Bentley also has a few examples of how badly things can go awry if you neglect to allow for the inherent failings of float arithmetic. The last book is great reading for anyone interested in programming, and is an entertaining and not too mind bending read.
I'm aware that this post is far more information than you asked for, but is enough for you to get a real handle on this stuff if you want more detail than "Never ever test floats for equality because it will bite you on the arse big time, cost you your job, kill innocent people and cause the collapse of banks, insurers and civilisation itself".
Enjoy,
John