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A parallel result in the nonincreasing case cannot be obtained using a similar argument as in Theorem 2.3 because the proof that (x n ) is a Cauchy sequence uses that xn-1and xn + pare comparable and this can be false when T is a nonincreasing operator (see, Theorem 2.3).
"Why is this so?" and "Is there any way this can be false?" are good questions for every statement, or claim.
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In addition, a large fraction of these can be false positives.
On local scales this assumption can be false, perhaps leading to small-scale variations being unintentionally smoothed out, in the dataset.
Since the impression must have been utterly convincing to him at the time at which he had it (judging by his subsequent action), it is clear from this that there can be false impressions which are indistinguishable from ones that are allegedly "stamped and impressed in accordance with that very thing" (Sextus Empiricus, 41H).
Omens can be false.
Mr. Acquisti, however, suggests that control can be false comfort.
But the lamentation of vanity can be false modesty.
But NASA knows too well that cheap missions can be false economies.
Sometimes, for example, there can be false positives that cause a great deal of anxiety.
"It can be false hope," said Tamara Estrella, the P.S. 24 parent coordinator.
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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