How do you use Hartogs in a sentence? See 2 example sentences showing how this word appears in different contexts, plus the exact meaning.
Hartogs meaning
plural of Hartog
Using Hartogs
- The main meaning on this page is: plural of Hartog
Context around Hartogs
- Average sentence length in these examples: 27.5 words
- Position in the sentence: 1 start, 1 middle, 0 end
- Sentence types: 2 statements, 0 questions, 0 exclamations
Corpus analysis for Hartogs
- In this selection, "hartogs" usually appears near the start of the sentence. The average example has 27.5 words, and this corpus slice is mostly made up of statements.
- Around the word, deeper, own and theorem stand out and add context to how "hartogs" is used.
- Recognizable usage signals include its own hartogs number this and much deeper hartogs theorem proves. That gives this page its own corpus information beyond isolated example sentences.
- By corpus frequency, "hartogs" sits close to words such as aabc, aacr and aacsb, which helps place it inside the broader word index.
Example types with hartogs
The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:
The much deeper Hartogs' theorem proves that the continuity hypothesis is unnecessary: f is holomorphic if and only if it is holomorphic in each variable separately. (26 words)
This is done by showing that n is smaller than which is smaller than its own Hartogs number — this uses the equality ; for the full proof, see Gillman (2002). (29 words)
This is done by showing that n is smaller than which is smaller than its own Hartogs number — this uses the equality ; for the full proof, see Gillman (2002). (29 words)
The much deeper Hartogs' theorem proves that the continuity hypothesis is unnecessary: f is holomorphic if and only if it is holomorphic in each variable separately. (26 words)
Example sentences (2)
The much deeper Hartogs' theorem proves that the continuity hypothesis is unnecessary: f is holomorphic if and only if it is holomorphic in each variable separately.
This is done by showing that n is smaller than which is smaller than its own Hartogs number — this uses the equality ; for the full proof, see Gillman (2002).