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

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The discussion focuses on formalizing the mathematical notation A >> B, which signifies that A is sufficiently larger than B. It emphasizes that this notation requires context to be meaningful, typically expressed in statements like "if n >> a, then P(n)." The discussion clarifies that this translates to "if n is sufficiently larger than a, then there exists an N such that if n > N + a, then P(n) holds true." The existence of N is crucial, as it underlines the conditions under which the statement is valid.

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given two real quantities A, B how can I formalize with reasonable rigour [tex]A>>B[/tex] ?
 
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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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