Intervals Meaning: Definition, Examples, and Translations
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intervals
[หษชntษrvษlz ]
Definition
mathematics
Intervals are sets of numbers between two given numbers. They can be open (not including the endpoints), closed (including the endpoints), half-open (including one endpoint but not the other), or half-closed (including one endpoint but not the other).
Synonyms
Which Synonym Should You Choose?
| Word | Description / Examples |
|---|---|
| intervals |
Use 'intervals' when talking about time periods or spaces between events or things. This word is often used in scheduling, music, and mathematics.
|
| range |
Use 'range' when talking about the extent or scope of something, often in a continuous sequence. It is common in discussions about prices, ages, temperatures, and various statistics.
|
| span |
Use 'span' when talking about the full extent or duration between two points, often in time or distance. It is also used to indicate how long something lasts or the physical distance something covers.
|
| segment |
Use 'segment' when referring to a part of a whole, usually a distinct section of something larger. This word is common in geometry, marketing, and various sciences.
|
Examples of usage
- An interval from 1 to 5 would include 1 but not 5.
- The interval (2, 7] includes all numbers from 2 to 7 except for 2.
- The interval [4, 9) includes all numbers from 4 to 9 except for 9.
Translations
To see the translation, please select a language from the options available.
Interesting Facts
Mathematics
- Intervals in math refer to the range of numbers between two endpoints, like the numbers that are between 1 and 5.
- In statistics, data intervals help summarize information, making it easier to understand patterns and trends.
Music
- In music, an interval is the distance between two notes. For example, the leap from C to E is called a major third.
- Intervals are foundational in creating melodies and harmonies, shaping how music sounds and feels.
Exercise & Fitness
- Interval training involves alternating between periods of intense effort and rest, leading to improved fitness levels.
- This type of training can boost metabolism and enhance endurance, making workouts more effective and efficient.
Linguistics
- In linguistics, intervals can describe timings in speech, such as the pauses between words or sentences that affect communication.
- Studying speech intervals helps in understanding rhythm and flow in spoken language, making it easier to learn new languages.
Philosophy
- Philosophically, intervals can represent the space between moments in time, prompting discussions on the nature of existence and temporality.
- The concept of intervals also leads to reflections on mindfulness, emphasizing the importance of appreciating each moment.
Origin of 'intervals'
The concept of intervals in mathematics dates back to ancient times, with early mathematicians using intervals to describe ranges of numbers. The formalization of intervals as sets came later, with contributions from mathematicians like Georg Cantor in the 19th century. Intervals play a crucial role in various branches of mathematics, such as calculus, analysis, and number theory.