Formalizing A>>B: How to Define and Use this Inequality in Mathematics?

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To formalize the inequality A >> B, it is essential to interpret it as A being sufficiently larger than B, though the term alone lacks clarity. This concept is often used in mathematical statements like "if n >> a, then P(n)," indicating that n must exceed a certain threshold for the statement P(n) to hold true. The formalization implies the existence of a specific N such that if n is greater than N + a, then P(n) is valid. However, the exact value of N is not defined, only that it exists. This approach allows for a rigorous understanding of the relationship between A and B in mathematical contexts.
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given two real quantities A, B how can I formalize with reasonable rigour A>>B ?
 
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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.
 
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