Meaning of (much greater)

[mnb96]

Hello,
given two real quantities A, B how can I formalize with reasonable rigour $$A>>B$$ ?

 

[disregardthat]

A>>B does not make sense by itself. It can be translated to A is sufficiently larger than B. By itself it does not state what it is sufficient to. Statements using >> are usually on the form "if n >> a, then P(n)", where a is some constant and P(n) is a statement about n. This statement can be translated to "if n is sufficiently larger than a, then P(n)", which means that "there exists an N such that if n > N+a, then P(n)". The N is not specified, the statement only says that such an N exists and P(n) is valid whenever n is larger than that.