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In the grading guide known as the Pavement Condition Index, zero is not far from a dirt strip and 100 is a fresh new roadway.
So, L is a Fredholm operator of index zero.
L is a Fredholm operator of index zero.
Then L is a Fredholm operator of index zero.
Clearly, L is a Fredholm operator with index zero.
whence the operator is Fredholm with index zero.
Let L be a Fredholm mapping of index zero.
Therefore, L is a Fredholm mapping of index zero.
Therefore, is a Fredholm mapping of index zero.
Therefore, is a Fredholm operator of index zero.
Therefore, L is a Fredholm operator of index zero.
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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