real number
Definition
- Noun:
- A real number is any number that can be found on the number line. This includes all rational numbers (like integers and fractions) and all irrational numbers (like √2 or π). It is a fundamental concept in mathematics used to represent continuous quantities.
Usage
- The term real number is used in mathematical contexts to distinguish these numbers from imaginary or complex numbers.
- It is often used when discussing the properties of numbers, solving equations, or describing sets of numbers.
- Example: "The solution to the equation must be a real number."
Examples
- Noun:
- 5, -3, 1/2, and 0 are all real numbers.
- The square root of 2 is an irrational real number.
- In calculus, we often work with functions defined for all real numbers.
Advanced Usage
- "The set of real numbers": Refers to the complete collection of all real numbers, often denoted by the symbol ℝ.
- The function is continuous for all values in the set of real numbers.
- "Real number line": A visual representation of real numbers as points on an infinitely long line.
- You can plot the inequality on the real number line.
Variants and Related Words
- Real (adjective): Pertaining to real numbers.
- We are looking for real solutions to the polynomial.
- Real Analysis (noun): A branch of mathematics dealing with real numbers and real-valued functions.
- Real Part (noun): In a complex number of the form a + bi, the component 'a' is the real part, which is a real number.
Synonyms
- Real (when used in a mathematical context, e.g., "real value").
- There are no perfect common-language synonyms for this precise mathematical term. Related concepts include scalar (in some contexts) or continuous quantity.
Related Phrases
- Real number system: The complete ordered field of real numbers.
- The properties of the real number system are axiomatic.
- Real-valued function: A function whose outputs are real numbers.
- f(x) = x² is a real-valued function.
Notes
- The term real number is specifically contrasted with imaginary number (based on the square root of -1) and complex number (which has both a real and an imaginary part).
- In non-mathematical contexts, "real" has different meanings (e.g., genuine, not artificial), but in this entry, only the mathematical definition is explained.
Noun
-
any rational or irrational number
Khám phá thêm
Các từ liên quan
Từ đồng nghĩa
