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The phrase 'for simplicity, we write' is correct and usable in written English
You can use it to introduce a simpler way to express something. For example: "The equation is quite long and complex, but for simplicity we write it as x + y = z."
Exact(31)
For simplicity we write (3.31).
For simplicity, we write Tx instead of (T x)).
For simplicity, we write and as one term.
For simplicity, we write (langlecdot,cdotrangle) and (|cdot|).
Proof For simplicity, we write T = T σ, τ.
For simplicity, we write (Gamma=Gamma_{k,N,mathbf{p}}).
Similar(28)
For the sake of simplicity we write instead of.
For the sake of simplicity, we write Φ ( m ) instead of Φ ∘ m.
For the sake of simplicity, we write V (n) = V (n, x(n)).
Remark 5 If φ is a function defined in Ω, then, for the sake of simplicity, we write T α ε instead of T α ε.
For the sake of simplicity, we write (a_{h_{i}}(cdot,cdot)) and (Vert cdot Vert _{h_{i}}) as (a_{h}(cdot,cdot)) and (Vert cdot Vert _{h}), in this paper.
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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