Your English writing platform
Discover LudwigExact(12)
Then (ii) We know that .
(ii) We know that,,, span.
By the assumption (ii), we know that.
By conditions (i) and (ii), we know that (2.2).
By step (II), we know is a KKM map.
Combining (i) and (ii), we know that can be listed as in (1.6).
Similar(48)
In World War II, we knew exactly what "unconditional surrender" meant -- victory!
On the other hand, by the proof of Theorem 3.1 (i - ii), we know that there exi - ii sequence (x n )n∈ℕof successive approximations for T starting from arbitrary (x0, x1) ∈ Graph(T ) weich converge to a fixed point x* ∈ X of the operator T. Since the fixed point is unique, we get that d(x n, x*) → 0 as n → +∞.
On the other hand, by Theorem 2.11(i - ii), we know that there exi - ii sequence ( x n ) n ∈ N of successive approximations for F starting from arbitrary ( x 0, x 1 ) ∈ Graph ( F ), weich converge to a fixed point x ∗ ∈ X of the operator F. Since, the fixed point is unique, we get that d ( x n, x ∗ ) → O as n → + ∞.
Their value is that they remind us of what we might otherwise take for granted: in this case, that Poland resisted Germany, thus beginning World War II as we know it, and as Roberts beautifully describes it.
Utilizing conditions (ii)–(iv), we know from (2.30) that (2.31).
Write better and faster with AI suggestions while staying true to your unique style.
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