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

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In summary, the conversation discusses how to formalize the expression A>>B, which means A is sufficiently larger than B. The statement is usually in the form of "if n >> a, then P(n)", where a is a constant and P(n) is a statement about n. This can be translated to "if n is sufficiently larger than a, then P(n)", indicating that there exists an N where if n > N+a, then P(n) is true. However, the value of N is not specified, only that it exists.
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mnb96
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Hello,
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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FAQ: Formalizing A>>B: How to Define and Use this Inequality in Mathematics?

1. What does "much greater" mean?

The phrase "much greater" typically refers to a significant difference or increase in quantity, size, or importance compared to something else. It can also imply a higher level of magnitude or intensity.

2. How is "much greater" different from "greater"?

"Much greater" is a comparative term that indicates a larger or more significant difference than the word "greater" alone. "Much" adds emphasis to the comparison and suggests a more substantial contrast between two things.

3. Can "much greater" be used to describe non-quantitative qualities?

Yes, "much greater" can be used to describe non-quantitative qualities, such as intelligence or beauty. In this context, it would signify a significant difference or degree of these qualities compared to others.

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The term "much greater" can be used subjectively or objectively, depending on the context. In some cases, it may be a subjective opinion, while in others, it may be supported by objective data or evidence.

5. How can "much greater" be measured or quantified?

"Much greater" can be measured or quantified by comparing the numerical values or qualities of two or more things. It can also be assessed through surveys, experiments, or other methods of data collection and analysis.

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