正無理數的意思、翻譯和例句

是什麼意思

「正無理數」是指大於零的無理數。無理數是不能被表示為兩個整數之比的數，這意味著它們的十進制表示是非循環且非終止的。常見的正無理數包括√2、π（圓周率）和e（自然對數的底數）。正無理數在數學中有重要的應用，尤其是在幾何學、數學分析和物理學等領域。

依照不同程度的英文解釋

  1. A number that cannot be written as a simple fraction and is greater than zero.
  2. A number that goes on forever without repeating and is positive.
  3. A positive number that cannot be expressed as a fraction.
  4. A number greater than zero that has a non-repeating decimal.
  5. A positive number that cannot be represented as a ratio of two integers.
  6. A positive irrational number that cannot be expressed as a fraction and has a non-terminating decimal expansion.
  7. A positive number whose decimal form is infinite and does not repeat, and cannot be expressed as a fraction.
  8. A positive non-rational number that cannot be simplified to a ratio of integers.
  9. A positive real number that cannot be expressed as the quotient of two integers and has a non-terminating, non-repeating decimal representation.
  10. A positive number that is not rational, meaning it cannot be expressed as a fraction, and has an infinite, non-repeating decimal expansion.

相關英文單字或片語的差別與用法

1：Positive irrational number

用法：

這個術語用來描述所有大於零且無法用兩個整數的比率表示的數。這些數在數學中非常重要，因為它們的特性使得它們在許多數學問題中出現，尤其是在幾何和代數中。正無理數的例子包括√2、√3及圓周率π。

例句及翻譯：

例句 1：

√2 是一個正無理數，因為它不能表示為兩個整數的比率。

√2 is a positive irrational number because it cannot be expressed as a ratio of two integers.

例句 2：

正無理數在計算圓的面積時非常重要。

Positive irrational numbers are very important in calculating the area of a circle.

例句 3：

許多數學家研究正無理數的性質。

Many mathematicians study the properties of positive irrational numbers.

2：Irrational number greater than zero

用法：

這個表達用來強調無理數的正值特性，特別是在數學分析或數學理論中。這類數在數學中經常用來解釋一些現象或計算。正無理數的例子包括圓周率π和自然對數的底數e。

例句及翻譯：

例句 1：

圓周率π是一個大於零的無理數，約等於3.14。

The number π is an irrational number greater than zero, approximately equal to 3.14.

例句 2：

自然對數的底數e也是一個正無理數。

The base of natural logarithms, e, is also an irrational number greater than zero.

例句 3：

在數學中，無理數大於零的特性對於理解數的結構非常重要。

In mathematics, the property of irrational numbers being greater than zero is crucial for understanding the structure of numbers.

輸入或選擇一個中文或英文單字或片語：