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The phrase "show the necessity" is correct and usable in written English.
You can use it when you want to demonstrate the importance of something or why something is necessary. For example, "Our research results showed the necessity of implementing a new training program for employees."
Exact(60)
But a concurring opinion contained the remark that the government should show the "necessity" of forcing reporters to testify.
But they will loudly demand a negotiation over something that is not open to compromise, namely a settled law from 2009 they disagree with because it will show the necessity of government's role in making health insurance available to all.
Protestant historians, on the other hand, portrayed the late medieval church in the most negative terms to show the necessity of the Reformation, which was characterized as a movement that broke completely with a corrupt past.
Let us show the necessity.
First, let us show the necessity.
To show the necessity part, suppose that E is an eigenvalue and Φ an associated eigenvector.
Computational experiments on those test problems clearly show the necessity of the normalization.
The results on the minus WFG4-9 show the necessity of normalization.
We show the necessity of short-term amplitude feedback when channel power imbalance is large.
Proof of Theorem A Obviously, we need only to show the necessity.
The following examples show the necessity of the conditions of Theorem 4.3.
More suggestions(16)
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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