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which follows that there exists vs which follows that there exist

Both phrases are correct, but they are used in different contexts. 'Which follows that there exists' is used when referring to a singular noun or entity, while 'which follows that there exist' is used when referring to multiple nouns or entities.

Last updated: March 19, 2024 • 561 views

which follows that there exists

This phrase is correct when referring to a singular noun or entity.

This phrase is used when you want to indicate the existence of a singular noun or entity following a certain condition or statement.

Examples:

  • The theory predicts a certain outcome, which follows that there exists a solution to the problem.
  • from which follows that there exists a c0 > 0 such that f(3k) = k + 1 = log3 3k + 1 ≥ ⌈log2 3k⌉. One could for example take c0 ∼ log2 3. 1) We will first show that ...
  • X* in S°; from which follows that there exists a subsequence of Xv, v = , 2, . .., converging towards X* for which distance (Xv, X*) < - always applies. Substituting .
  • has at least one solution. Hence, we can apply the 'afiine' form of Farkas' lemma. (in [Sch86]), from which follows that there exists 66 and (5' such that 66 2 50,.
  • May 1, 2012 ... Hence, it is easy to show that which follows that there exists a positive quantity such that for all large . It proves the boundedness of positive ...

Alternatives:

  • which implies that there exists
  • which means that there exists
  • which shows that there exists
  • which indicates that there exists
  • which suggests that there exists

which follows that there exist

This phrase is correct when referring to multiple nouns or entities.

This phrase is used when you want to indicate the existence of multiple nouns or entities following a certain condition or statement.

Examples:

  • The data supports the hypothesis, which follows that there exist multiple solutions to the problem.

Alternatives:

  • which implies that there exist
  • which means that there exist
  • which shows that there exist
  • which indicates that there exist
  • which suggests that there exist

Related Comparisons

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