ことなく details
write + without ever doing X — a written-register span across which X never once occurred
kaku koto naku
without ever doing X — a written-register span across which X never once occurred
meaning: without ever writing
彼は一度も諦めることなく、挑戦し続けた。
kare wa ichido mo akirameru koto naku, chousen shitsuzuketa.
He kept up his challenge, without ever giving up even once. neutral
彼女は誰にも頼ることなく、一人でその困難を乗り越えた。
kanojo wa dare ni mo tayoru koto naku, hitori de sono konnan o norikoeta.
She overcame that hardship alone, without ever relying on anyone. formal
Examples
without ever doing X — a written frame spanning an entire stretch across which the act never once occurred
彼は一度も諦めることなく、挑戦し続けた。
kare wa ichido mo akiramerukotonaku, chousen shitsuzuketa.
He kept up his challenge, without ever giving up even once. neutral
彼女は誰にも頼ることなく、一人でその困難を乗り越えた。
kanojo wa dare ni mo tayoru koto naku, hitori de sono konnan o norikoeta.
She overcame that hardship alone, without ever relying on anyone. formal
会議は特に問題が起きることなく終わった。
kaigi wa toku ni mondai ga okiru koto naku owatta.
The meeting ended without any problems ever arising. neutral
Formation
{V}ことなくattaches to dictionary form
Related patterns
Similar
Both are the written register's "without doing", but ことなく frames an entire SPAN across which the act never once occurred — often paired with 一度も — while ずに is the plain written substitute for ないで with no durational claim at all.
ないで is the everyday spoken default for "without doing" and attaches as a simple manner adjunct; ことなく never occurs in speech, reads stiff even in writing if overused, and typically frames the whole sentence's outcome rather than one small manner detail.