# Definitions for supremumsupre·mum

### Wiktionary(0.00 / 0 votes)Rate this definition:

1. supremum(Noun)

(of a subset) the least element of the containing set that is greater or equal to all elements of the subset. The supremum may or may not be a member of the subset.

### Freebase(0.00 / 0 votes)Rate this definition:

1. Supremum

In mathematics, the supremum of a subset S of a totally or partially ordered set T is the least element of T that is greater than or equal to all elements of S. Consequently, the supremum is also referred to as the least upper bound. If the supremum exists, it is unique meaning that there will be only one supremum. If S contains a greatest element, then that element is the supremum; otherwise, the supremum does not belong to S. For instance, the negative real numbers do not have a greatest element, and their supremum is 0. The existence or non-existence of a supremum is often discussed in connection with subsets of real numbers, rational numbers, or any other well-known mathematical structure for which it is immediately clear what it means for an element to be "greater-than-or-equal-to" another element. The definition generalizes easily to the more abstract setting of order theory, where one considers arbitrary partially ordered sets. The concept of supremum coincides with the concept of least upper bound, but not with the concepts of minimal upper bound, maximal element, or greatest element. The supremum is in a precise sense dual to the concept of an infimum.

1. supermum

1. Alex
US English
Daniel
British
Karen
Australian
Veena
Indian

### Numerology

1. Chaldean Numerology

The numerical value of supremum in Chaldean Numerology is: 2

2. Pythagorean Numerology

The numerical value of supremum in Pythagorean Numerology is: 9

### Popularity rank by frequency of use

supremum#100000#128302#333333

### Translation

#### Find a translation for the supremum definition in other languages:

Select another language:

• - Select -
• 简体中文 (Chinese - Simplified)
• Español (Spanish)
• Esperanto (Esperanto)
• 日本語 (Japanese)
• Português (Portuguese)
• Deutsch (German)
• العربية (Arabic)
• Français (French)
• Русский (Russian)
• 한국어 (Korean)
• עברית (Hebrew)
• Український (Ukrainian)
• اردو (Urdu)
• Magyar (Hungarian)
• मानक हिन्दी (Hindi)
• Indonesia (Indonesian)
• Italiano (Italian)
• தமிழ் (Tamil)
• Türkçe (Turkish)
• తెలుగు (Telugu)
• ภาษาไทย (Thai)
• Tiếng Việt (Vietnamese)
• Čeština (Czech)
• Polski (Polish)
• Bahasa Indonesia (Indonesian)
• Românește (Romanian)
• Nederlands (Dutch)
• Ελληνικά (Greek)
• Latinum (Latin)
• Svenska (Swedish)
• Dansk (Danish)
• Suomi (Finnish)
• فارسی (Persian)
• ייִדיש (Yiddish)
• հայերեն (Armenian)
• Norsk (Norwegian)
• English (English)

## Citation

#### Use the citation below to add this definition to your bibliography:

Style:MLAChicagoAPA

"supremum." Definitions.net. STANDS4 LLC, 2020. Web. 10 Apr. 2020. <https://www.definitions.net/definition/supremum>.

## Are we missing a good definition for supremum? Don't keep it to yourself...

#### Free, no signup required:

Get instant definitions for any word that hits you anywhere on the web!

#### Free, no signup required:

Get instant definitions for any word that hits you anywhere on the web!