N2
ことなく
Without ~ing
遅刻することなく、職場に着いた。
I was able to arrive at work without being late.
Explanation
Follows the dictionary form of a verb and means 'without ...ing', like 「ないで」 or 「ずに」 but more formal and written. Throughout the whole process, something that might have happened never did: 「休むことなく働き続けた」 (He kept working without a break); 「迷うことなく決断した」 (She decided without hesitation). A continuing action or a smooth result usually follows.
Mixed up with
The forms differ: 「ことなく」 follows the dictionary form (諦めることなく); 「ないで/ずに」 follow the ない form (諦めないで/諦めずに). Tests like to trap you here.
「ことなく」 reads as literary, used in biographies, speeches and reports: 「希望の光は絶えることなく輝き続けた」 (The light of hope kept shining without fading).
「ないで」 fits everyday matters: 「傘を持たないで出かけた」 (I went out without an umbrella).