Can equality of two real number be defined within a tolerance? Say, 0 = 0.000009 given the tolerance to be 0.00001. I also assume that equality should be transitive, e.g. a = b, b = c, then a = c. But, seems it is not always the truth.
Sometimes, I want two real numbers to be considered as equal as long as they are close enough, and also want this kind of equality to be transitive. Can it be possible?
(Not sure what tags should I put)