unconditionally summable (english) - meaning, definition, translation, pronunciation

Part of Speech

Adjective

Phonetic Transcription

/ˌʌn.kənˈdɪʃ.ən.əl.i ˈsʌm.ə.bəl/

Meaning and Usage

The term "unconditionally summable" refers to a mathematical property of a series or a sequence where the series or sequence converges regardless of the arrangement of its terms. It indicates that the sum of a series converges to a finite limit without any conditions placed on its summation order.

In mathematical contexts, particularly in functional analysis and related fields, this term is more frequently used in written contexts, especially in scholarly articles, textbooks, and advanced mathematical discussions. Its use in spoken language is relatively less common since it is a specialized term.

Example Sentences

1. The series defined by the harmonic numbers is not unconditionally summable.

2. Серия, определяемая гармоническими числами, не является безусловно суммируемой.

3. In functional analysis, we often deal with unconditionally summable sequences.

4. В функциональном анализе мы часто имеем дело с безусловно суммируемыми последовательностями.

5. The properties of unconditionally summable series are crucial for understanding convergence behaviors.

6. Свойства безусловно суммируемых рядов имеют решающее значение для понимания поведения сходимости.

Idiomatic Expressions

While "unconditionally summable" itself is not commonly integrated into idiomatic expressions, its components can be found in various mathematical remarks or discussions. Here are a few expressions related to "summable" that are used in mathematical contexts:

1. Summable series: A series that converges to a limit.
2. Пример: The series is known to be summable.

3. The series is known to be summable. - Известно, что серия является суммируемой.

4. Absolutely summable: A stronger form where the series of absolute values converges.

5. Пример: An absolutely summable sequence guarantees stability.

6. An absolutely summable sequence guarantees stability. - Абсолютно суммируемая последовательность гарантирует стабильность.

7. Geometrically summable: Refers to a series whose terms can be summed using geometric series techniques.

8. Пример: The terms of the series are geometrically summable.
9. The terms of the series are geometrically summable. - Члены ряда можно геометрически суммировать.

Etymology

The term "unconditionally summable" derives from the prefix "un-" indicating negation, the root "condition," and "summable" which comes from “sum” (from Latin "summare") meaning to add up. The use of "summable" indicates the ability to total a series of numbers or elements.

Synonyms and Antonyms

• Synonyms: Convergent series (in a general sense, though not strictly synonymous), absolutely summable (a stronger condition).
• Antonyms: Divergent series, conditionally summable (where convergence depends on the arrangement of terms).