How Do You Spell SUPREMUM?

Pronunciation: [suːpɹˈɛməm] (IPA)

Supremum is a mathematical term that describes the least upper bound of a set. The correct spelling of this word is /sjuːˈpriːməm/, with the stress on the second syllable. The IPA phonetic transcription shows that the first syllable starts with the consonant cluster /sjuː/, which is pronounced as "s-yoo". The next two syllables are pronounced as "pree-muhm". Remembering the correct spelling and pronunciation of technical terms like supremum is crucial for effective communication in mathematics and other fields.

SUPREMUM Meaning and Definition

1. Supremum is a mathematical term that refers to the upper bound of a set. Specifically, in the context of ordered sets, it represents the smallest element that is greater than or equal to all the elements in the set. The word "supremum" comes from the Latin word "supremus," meaning highest or topmost.

   To understand supremum, we need to consider partially ordered sets. A partially ordered set is a set where there exists a relation that compares the elements, but not all elements can be compared. In such cases, supremum is used to define the least upper bound.

   In a set, if there is an element that is greater than or equal to every other element in the set, it is the supremum of that set. However, the supremum may not always be part of the set. For example, in the set of real numbers less than or equal to 1, the supremum is 1. Another example is the set of positive real numbers, which has no supremum because there is no greatest element.

   Supremum is an important concept in mathematical analysis, particularly in studying limits and convergence. It helps define the completeness of a set or metric space. Moreover, it plays a vital role in the concept of infimum, which is the greatest lower bound of a set.

Common Misspellings for SUPREMUM

• aupremum
• zupremum
• xupremum
• dupremum
• eupremum
• wupremum
• sypremum
• shpremum
• sjpremum
• sipremum
• s8premum
• s7premum
• suoremum
• sulremum
• su-remum
• su0remum
• supeemum
• supdemum
• supfemum
• suptemum

Etymology of SUPREMUM

The word "supremum" has its origins in Latin. It is formed from the combination of two Latin words: "supremus" meaning "highest" or "topmost", and "-um", a suffix often used to form nouns. "Supremus" itself is the superlative form of "superus", meaning "above" or "over". Therefore, "supremum" can be understood to mean "the highest" or "the topmost". In mathematics, "supremum" refers to the least upper bound of a set, reflecting its meaning of being the highest or topmost value.