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The phrase "a realizing" is not correct and usable in written English.
It is typically used in contexts where one is referring to the act of becoming aware or understanding something, but it is more common to use "realization" instead.
Example: "The sudden realizing of her mistake made her feel embarrassed."
Alternatives: "an awareness" or "a recognition".
Exact(2)
But we then proceed to define |A| (the cardinality of a set A) as the set of all sets which are the same size as A, realizing the definition intended by Frege and Russell, and apparently intended by Cantor as well.
Recognizing the absolute other within constitutes not simply a reflexive self-awareness but a self-awakening, a realizing of the "true self".
Similar(55)
B and A realize two-way authentication.
Hemingway was a master not of a realized stoicism but of a wounded epicureanism.
A realized loss occurs when an asset is sold for less than it cost to acquire.
The other mistake is to cash in winners for the psychic satisfaction of a realized gain.
The life sciences sector in Finland has suffered from a realized political risk.
Therefore, in a realized scenario, the facilities can be divided into normal and disrupted facilities (DF).
In such cases, changes to one or more properties that jointly realize a realized property G are compensated for by changes in others of the jointly realizing properties.
First, we estimate a realized relationship matrix based on aggregate SNP information [ 16- 18].
When you become a realized master, then you can dispute for others' benefit, not before.
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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