How Do You Spell BOUNDED INTERVAL?

Pronunciation: [bˈa͡ʊndɪd ˈɪntəvə͡l] (IPA)

The phrase "bounded interval" in mathematics refers to a set of numbers between two given values, where each number within the set is finite. The spelling of "bounded interval" in IPA phonetic transcription is /ˈbaʊndɪd ˈɪntəvəl/. The stress is on the first syllable of both words, and "bounded" is pronounced with the same sound as "round". "Interval" includes a vowel sound that's similar to "win" with an emphasis on the second syllable. This phrase is important in calculus, probability theory, and other fields of mathematics.

BOUNDED INTERVAL Meaning and Definition

1. A bounded interval refers to a specific type of interval in mathematics, commonly used in the field of real analysis. An interval is a set of real numbers that lie between two boundary points. When an interval has both a minimum and a maximum value, it is considered a bounded interval.

   Formally, a bounded interval is defined as a set of real numbers that includes all the numbers that are between or equal to two given values, called the endpoints or boundary points. These boundary points indicate the limits of the interval. The smaller value between the two endpoints is typically referred to as the lower bound, while the larger value is called the upper bound.

   For example, consider the interval [1, 5]. In this case, 1 is the lower bound of the interval, while 5 is the upper bound. The interval contains all real numbers between and including 1 and 5. It can be represented using interval notation as [1, 5], or in set notation as {x∈ℝ | 1 ≤ x ≤ 5}.

   Contrarily, an unbounded interval has one or both endpoint(s) that either approaches infinity (∞) or negative infinity (-∞). These unbounded intervals have no specified limit, as the interval keeps extending indefinitely in either the positive or negative direction along the real number line.

Common Misspellings for BOUNDED INTERVAL

• vounded interval
• nounded interval
• hounded interval
• gounded interval
• biunded interval
• bkunded interval
• blunded interval
• bpunded interval
• b0unded interval
• b9unded interval
• boynded interval
• bohnded interval
• bojnded interval
• boinded interval
• bo8nded interval
• bo7nded interval
• boubded interval
• boumded interval
• boujded interval

Etymology of BOUNDED INTERVAL

The word "bounded" comes from the verb "bound", which in this context means to limit, restrict, or define the range or extent of something. It derives from the Old French word "bonder", meaning "to limit" or "to gather". The noun "interval" comes from the Latin word "intervallum", which was composed of the prefix "inter-" meaning "between" and the noun "vallum" meaning "rampart" or "wall". Therefore, the word "bounded interval" refers to a range or segment that is defined or limited by a specific starting and ending point.