Pronunciation: [ɹˈi͡əlz] (IPA) 
The word "reals" is a plural form of the noun "real". The pronunciation of the word is /rɪəlz/ in IPA phonetic transcription. The first sound in the word is a voiced alveolar fricative /r/. The second sound is an unstressed schwa /ɪə/. The third sound is a voiced alveolar fricative again /l/, followed by the plural marker sound /z/. The spelling of the word "reals" follows the basic rule of adding "-s" to form the plural of most nouns.
The term "reals" can be defined as the plural form of the noun "real," referring to a mathematical concept and number system known as the real numbers. The real numbers encompass all rational and irrational numbers, forming an infinite set that includes integers, fractions, decimals, and infinite decimals, as well as numbers such as π (pi) and √2 (the square root of 2). In other words, the reals consist of any numerical value that can be represented on the number line.
Unlike other number systems, the real numbers possess certain properties that make them unique. They exhibit a total order, allowing for comparisons between any two numbers, which is reflected in their ability to be arranged in ascending or descending order. Additionally, the reals possess the property of completeness, meaning that any non-empty set of real numbers bounded from above has a least upper bound and any set bounded from below has a greatest lower bound.
The real numbers are widely used in various fields of mathematics and science, serving as the foundation for calculus, analysis, and other branches of advanced mathematics. They provide a comprehensive framework for measuring quantities and performing calculations in a continuous manner, making them an indispensable tool in many real-world applications.
The word "reals" is derived from the noun "real" which originates from the Latin word "realis". The Latin word "realis" comes from the noun "res" meaning "thing" or "matter". Over time, "realis" evolved into "real" in Late Latin, and further developed in Old French as "reel" meaning "real" or "true". It eventually entered the English language as "real" in the 14th century. "Reals", being the plural form of "real", is used to describe the set of real numbers in mathematics.
