different between manifold vs differentiable

English

Alternative forms

• manyfold

Pronunciation

• (General American) IPA^(key): /?mæn??fo?ld/, (nonstandard) /?m?n??fo?ld/, /?m?ni?fo?ld/
• (Received Pronunciation) IPA^(key): /?mæn??f??ld/
• Hyphenation: man?i?fold
• Rhymes: -æn?fo?ld

Etymology 1

From Middle English manifold, from Old English mani?feald (“manifold, various, varied, complicated, numerous, abundant, plural”), from Proto-Germanic *managafalþaz, equivalent to many +? -fold. Cognate with Middle High German manecvalt (“manifold”), Icelandic margfaldr (“multiple”). Compare also German mannigfaltig (“various”), Dutch menigvoudig (“various”), Danish mangefold (“multiple”), Swedish mångfald (“diversity”).

Adjective

manifold (comparative more manifold, superlative most manifold)

1. Various in kind or quality; diverse.

2. Many in number, numerous; multiple, multiplied.
3. Complicated.
4. Exhibited at diverse times or in various ways.
   • c. 1384, I Petre 4:10 (Wycliffe's Bible):

     ... the manyfold grace of God.

   • 1611, Ephesians 3:10 (w:King James Bible):

     The manifold wisdom of God.

Synonyms

• (various in kind or quality): diverse, various, varied, multiplicitous; See also Thesaurus:heterogeneous
• (many in number): multiple, numerous; see also Thesaurus:manifold

Antonyms

• onefold
• singlefold

Derived terms

• manifolder
• manifoldly
• manifoldness

Translations

Adverb

manifold (comparative more manifold, superlative most manifold)

1. Many times; repeatedly.

Synonyms

• manyfold, frequently, ofttimes; see also Thesaurus:often

Noun

manifold (plural manifolds)

1. (historical) A copy made by the manifold writing process.
2. (mechanics) A pipe fitting or similar device that connects multiple inputs or outputs.
3. (US, regional, chiefly in the plural) The third stomach of a ruminant animal, an omasum.
   • 1830 Anson, Somerset Co. Me., accessed 12 June 2007

     My conjecture being right he will find the third stomach, or manifolds, the seat of difficulty.

4. (mathematics) A topological space that looks locally like the "ordinary" Euclidean space ${\displaystyle \mathbb {R} ^{n}}$ and is Hausdorff.
5. (computer graphics) A polygon mesh representing the continuous, closed surface of a solid object

Usage notes

In mathematics, a manifold of some number of dimensions n is termed an n-manifold (e.g. 3-manifold).

Hyponyms

Derived terms

Translations

Etymology 2

From Middle English manifolden, from Old English mani?fealdan (“to multiply, abound, increase, extend, reward”), equivalent to many +? -fold. Cognate with Middle High German manecvalten, Icelandic margfalda (“to multiply”), Swedish mångfaldiga (“to manifold, reproduce”).

Verb

manifold (third-person singular simple present manifolds, present participle manifolding, simple past and past participle manifolded)

1. (transitive) To make manifold; multiply.
2. (transitive, printing) To multiply or reproduce impressions of by a single operation.

Translations

English

Etymology

From differentiate +? -able

Pronunciation

• (UK) IPA^(key): /?d?f.?(?)??n.??.b?l/

Adjective

differentiable (comparative more differentiable, superlative most differentiable)

1. (calculus, not comparable) Having a derivative, said of a function whose domain and codomain are manifolds.
2. (comparable, of multiple items) able to be differentiated, e.g. because they appear different

Related terms

• differentiability

Translations

Danish

Adjective

differentiable

1. plural and definite singular attributive of differentiabel