Rather than saying a variable is “small,” we might say it is much less than 1. ![]() The ratio b/a = 0.03, and your error should be small relative to 0.03, so the approximation above should be good enough. Suppose you need to know √103 to a couple decimal places. If, in your context, you decide that b/ a is small, the approximation error will be an order of magnitude smaller. So when is | b| much less than a? That’s up to you. You might see somewhere that for | b| ≪ a, the following approximation holds: All jargon is like this.īelow are some examples of ≪ and ≫ in practice. You have to know the context to understand how to interpret them, but they’re very handy if you are an insider. The symbols ≪ and ≫ can make people uncomfortable because they’re insider jargon. Sometimes you’ll see ≫, or more likely > (two greater than symbols), as slang for “is much better than.” For example, someone might say “prototype > powerpoint” to convey that a working prototype is much better than a PowerPoint pitch deck. Is 5 much less than 7? It is if you’re describing the height of people in feet, but maybe not in the context of prices of hamburgers in dollars. Here’s a little table showing how to produce the symbols. ![]() The symbol ≪ means “much less than, and its counterpart ≫ means “much greater than”. The symbols ≪ and ≫ may be confusing the first time you see them, but they’re very handy.
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