It’s often harder to tell from context when something is large than when it is small. The error in the example is more than 30,000, but this value is small relative to 10! = 3,628,800. The relative error is small, not the absolute error. Note that the approximation error above is small relative to the exact value. For instance, if n = 10, the approximation above has an error of less than 1%. For example, Stirling’s formula for factorials saysįor n ≫ 1. Sometimes you see something like n ≫ 1 to indicate that n must be large. How small is small enough? The post explains how to know. A lot of people memorize “You can replace sin θ with θ for small angles” without thoroughly understanding what this means. If θ is small, the error in the approximation above is very small.Ī few years I wrote a 700-word blog post unpacking in detail what the previous sentence means. 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”. Wood Foundation, Bank of America, N.A.The symbols ≪ and ≫ may be confusing the first time you see them, but they’re very handy. Example 4įunded by a grant from the William M. The sign of comparison is used whenever the symbol appears in print. The numeric indicator is required before a numeral that follows a sign of comparison. Greater than or equal to is formed with dots four five six in the first cell, dot four in the second cell, and dots three four five in the third cell.Ī blank space is left before and after the sign of comparison. Less than or equal to is formed with dot four five six in the first cell, dot four in the second cell, and dots one two six in the third cell. Less than or equal to and greater than or equal to are each formed with three cells. Greater than is formed with a dot four prefix and dots three four five in the root cell. Less than is formed with a dot four prefix in the first cell and dots one two six root in the second cell. Like the equals sign, both symbols are formed with a prefix and a root. The symbols for opening angle bracket and closing angle bracket are used in print to represent less than and greater than respectively. One of the design features of UEB is that each print symbol has one and only one braille representation. Lesson 1.5: Symbols of Comparison: Less Than, Greater Than, Less Than or Equal To, Greater Than or Equal To Symbols
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