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"the first order" is a grammatically correct phrase that can be used in written English.
It is often used to refer to the initial or primary command or request given in a situation. For example: - The judge issued the first order of the trial, asking the witnesses to take the stand. - The first order of business at the meeting was to elect a new president. - After completing the first order, the chef moved on to prepare the second course. In these examples, "the first order" refers to the first task or action in a sequence of events. It can also be used in a military context, referring to the first set of instructions given to soldiers or units.
Exact(55)
The first order, he said, "worked out.
(c) The first order derivatives.
An indulgence of the first order.
It's baloney of the first order!
"The first order was for $50,000".
That's the first order of business.
Similar(5)
(b) The first-order correlation function dynamics.
In the first-order case, it reduces to linear interpolation.
The first-order rate model.
k1 is the first-order rate constant.
where denotes the first-order derivative of.
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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