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from which follows that there exists vs which follows that there exists

Both phrases are correct, but they are used in different contexts. 'From which follows that there exists' is more formal and structured, suitable for academic or technical writing. 'Which follows that there exists' is a simpler version that can be used in everyday language.

Last updated: March 19, 2024 • 769 views

from which follows that there exists

This phrase is correct and commonly used in formal writing to introduce a conclusion or consequence.

This phrase is typically used in formal or academic writing to introduce a logical consequence or conclusion that can be deduced from the preceding information.

Examples:

  • The theory, from which follows that there exists a solution, has been widely accepted.
  • From which follows that there exists a direct correlation between the two variables.
  • The data, from which follows that there exists a pattern, was carefully analyzed.
  • From which follows that there exists a need for further investigation.
  • The experiment, from which follows that there exists a significant result, was repeated multiple times.
  • 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,.
  • Aug 8, 2001 ... Rm(A) = 0. (57). Let us assume that Rm(A) = 0, from which follows that there exists an eigenvector e of. Rm(A) such that. Rm(A) e = σ e, σ = 0.

Alternatives:

  • Therefore, there exists
  • Consequently, there exists
  • Hence, there exists
  • Thus, there exists
  • As a result, there exists

which follows that there exists

This phrase is correct and can be used in everyday language to express a logical consequence or conclusion.

This phrase is suitable for informal or everyday language to indicate a conclusion or result that can be inferred from the previous information.

Examples:

  • He missed the deadline, which follows that there exists a penalty.
  • She failed the test, which follows that there exists a need for extra study.
  • The car broke down, which follows that there exists a need for repairs.
  • The budget was exceeded, which follows that there exists a financial issue.
  • The project was successful, which follows that there exists a celebration.
  • 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:

  • Therefore, there exists
  • Consequently, there exists
  • Hence, there exists
  • Thus, there exists
  • As a result, there exists

Related Comparisons

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