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The phrase "a first example is" is correct and usable in written English.
It can be used when introducing an initial instance or illustration of a concept or argument you are discussing.
Example: "In discussing the impact of climate change, a first example is the increase in global temperatures over the past century."
Alternatives: "an initial example is" or "a primary example is".
Exact(9)
A first example is a project called "Open Worm".
A first example is to provide to the customers a visualization of their typical temporal purchasing patterns to make them conscious of their behavior.
A first example is that bus accident severity reaches higher levels and injury occurrence on-board becomes more likely when both the buses and the third parties proceed straight with respect to when they either stand or turn.
A first example is the FIX Trading Community, which established and maintains the FIX trading standard, now the standard used internationally for buy- and sell-side financial services companies.
A first example is the vector space ℓ p consisting of infinite vectors with real entries whose p-norm given by :|\mathbf x|_p := \left(\sum_i |x_i|^p \right)^{1/p} for p < ∞ and |\mathbf x|_\infty := \text{sup}_i |x_i| is finite.
A first example is that the panel recommended focal therapy for men with intermediate-risk PCa.
Similar(51)
A second example is average earnings.
A second example is a plate with distributed hard inclusions.
A third example is the Columbia Acorn International fund.
A second example is warnings related to mercury in seafood.
A second example is the spherical shell with specified temperatures and, as sketched in Figure 16.11.
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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