“absolute value”的概念、定义、翻译、参考文献-科学参考

absolute value

Physics

The square root of the sum of the squares of the real numbers in a complex number, i.e. the absolute value of the complex number z=x + iy is $| z | = \sqrt (x^{2} + y^{2})$ .

Mathematics

For any real number $a$ , the absolute value (also called the modulus) of $a$ , denoted by $| a |$ , is $a$ itself if $a \geq 0$ , and $- a$ if $a \leq 0$ . Thus $| a |$ is positive except when $a = 0$ . The following properties hold:
1. (i) $| a b | = | a | | b | .$
2. (ii) $| a + b | \leq | a | + | b | .$
3. (iii) $| a - b | \geq | | a | - | b | | .$
4. (iv) For $a > 0$ , $| x | \leq a$ if and only if $- a \leq x \leq a$ .
(ii) is the triangle inequality and (iii) is sometimes known as the reverse triangle inequality.

Graph of absolute value

Statistics

The value of a number disregarding its sign. Denoted by a pair of ‘|’ signs: thus the modulus of −2.5 is |−2.5 |=2.5.

Computer

The magnitude of a number, regardless of its sign (positive or negative). For example, 25 is the absolute value of 25 and −25. Most spreadsheet programs include a function that returns the absolute value of a number.

单词	absolute value
释义	absolute value Physics The square root of the sum of the squares of the real numbers in a complex number, i.e. the absolute value of the complex number z=x + iy is $\| z \| = \sqrt (x^{2} + y^{2})$ . Mathematics For any real number $a$ , the absolute value (also called the modulus) of $a$ , denoted by $\| a \|$ , is $a$ itself if $a \geq 0$ , and $- a$ if $a \leq 0$ . Thus $\| a \|$ is positive except when $a = 0$ . The following properties hold: (i) $\| a b \| = \| a \| \| b \| .$ (ii) $\| a + b \| \leq \| a \| + \| b \| .$ (iii) $\| a - b \| \geq \| \| a \| - \| b \| \| .$ (iv) For $a > 0$ , $\| x \| \leq a$ if and only if $- a \leq x \leq a$ . (ii) is the triangle inequality and (iii) is sometimes known as the reverse triangle inequality. Graph of absolute value Statistics The value of a number disregarding its sign. Denoted by a pair of ‘\|’ signs: thus the modulus of −2.5 is \|−2.5 \|=2.5. Computer The magnitude of a number, regardless of its sign (positive or negative). For example, 25 is the absolute value of 25 and −25. Most spreadsheet programs include a function that returns the absolute value of a number.
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