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There are three main outcomes due to omission of this active experimentation phase: First, on an individual basis it may not be possible for the learner to apply the concluded principles in a safe environment, without facing the risk of real adverse outcomes and reactions.
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Those charges that might apply, the lawyers concluded, would either be too difficult to prove, too minor or, in the case of the federal prosecutors, only possible against Mr. Bruder.
The researchers also reconstructed tools that could have been used to apply the pigment, and concluded that the stripes were made by a primitive crayon with a tip that measured about one to three millimeters in diameter.
In the same manner, we can apply the condition to conclude that (3.37).
Similarly, we apply the LLN to conclude that 1 N ∑ i = 1 N P ( R s | X i ) → p P ( R s ).
Since maps into and restricted to is invertible, we can apply the preceding proof and conclude that the sequence as defined before converges to and.
Since maps into and restricted to is invertible, we can apply the preceding proof and conclude that the sequence converges to and.
"Because the transactions between you and DCM were commercial transactions conducted on terms available to the general public without being apparently specifically designed to provide personal benefit to you, neither the gift limit nor the gift disclosure requirements of the Act will apply," Korchmaros concluded.
We can then apply the classical Zorn lemma to conclude and the proof of the theorem is complete.
Therefore, in the last four cases, we may apply the first two cases to conclude our proof.
This convergence enables us to apply the Weierstrass M-test to conclude that a series ∑ k = 1 ∞ ∥ ϕ i ( t ) − ϕ i − 1 ( t ) ∥ (5.2). converges uniformly on I. Also, we can write ϕ k ( t ) as the following sum ϕ k ( t ) = ϕ 0 ( t ) + Σ i = 1 k ( ϕ i ( t ) − ϕ i − 1 ( t ) ). (5.3).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com