〜ことなく
without (ever) doing
Verb dictionary form + ことなく
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ことなく means "without doing", like ずに and ないで, but more formal and emphatic: 彼は休むことなく働き続けた, "he kept working without a single break".
It follows the dictionary form of a verb. It often implies something that might have been expected didn't happen at all: 一度も失敗することなく, "without failing even once"; 迷うことなく, "without a moment's hesitation".
It's typical of writing, speeches and news. In conversation, ずに or ないで is more natural.
A related form, ことなしに, means "without doing (it's impossible)": 努力することなしに、成功はない, "there's no success without effort".
Examples
彼は休むことなく働き続けた。
He kept working without a single break.
一度も失敗することなく、最後までやり遂げた。
I saw it through to the end without failing even once.
迷うことなく、この道を選んだ。
I chose this path without hesitation.
雨の日も休むことなく、毎日走っている。
I run every day without fail, even when it rains.
誰にも知られることなく、町を出た。
I left town without anyone knowing.