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〜ず
zu, zuni
JLPT N2
Edit  bi-ru
Meaning
Without (doing)
Without thinking
Edit  bi-ru
Formation
Verb ~ない form without ない
+
Edit 
See also
Phrases
おもわずはだしでそとにでた。
Without thinking I went outside barefoot .
Edit  #3216 bi-ru
おんなだとまちがえずはたらきやがって!なリモコンだ!
For a woman, this damn thing works without a mistake! Pervy remote control!
Edit  #3217 bi-ru
にほんごをおぼえずににほんでのクラス(じゅぎょう)はむずかしい。
Classes are hard in Japan without remembering Japanese
Edit  #5525 cup
なぜあなたはくわずぎらいになったのか
Why have you turned into a such a person who criticizes before trying?
Edit  #5526 blabby
にほんごをおぼえずに、にほんでくらすのはむずかしい。
It is hard to live in Japan without mastering the Japanese language.
Edit  #5529 Miki
あいをしんじられずにそだったは、はたらきながらだいがくにかようくがくせい。
Brought up without believing in love, Kan Jeho supports herself working while going to college.
Edit  #5536 dc
あめがふらず、かわのみずがひあがった
With no rain, the water in the river dried up.
Edit  #7081 Phenie
こまっているひとをみたら、たすけずにはいられない。
If I see worried people, I can't help but rescue them .
Edit  #6710 赤毛
あまりしょうらいのことをかんがえずにこのしごとをえらんだばかりに、こんくろうばかりしている。
Just after choosing this job almost without thinking about the future, I only have troubles now.
Edit  #6711 赤毛
このぬのはみずにつよいはんめん、ねつにはよわい。
This cloth seems strong without trying but weak in the action.
Edit  #6712 赤毛
Discussion and comments
あ-Stem + ず

It means _without_, it is formed by the [NegativeForm] + zu" and means "without doing".

"~zu ni" is the same as "~nai de".
cup
although i'm not sure of the actual probability of native speakers using such a phrasing, strictly grammatically speaking, 信じられざる話 would be the correct form. in traditional japanese grammar, ず is called 終止形 (collective term for verbs and adjectives at the end of sentences). the 連体形 (modifying nouns (体言)) of ず is ざる. in modern japanese, the 終止形 (ない) and the 連体形 (ない) are the same, so one doesn't think in those terms most of the time, but when using lingering elements from classical japanese, they are important. however, ざる-ending expressions, though not restricted to written japanese, have a rather formal sound to them.
rasmusjp
nice example bi-ru!
dc
Vn denotes Verb negative base.

i.e.

yomu -> yoma(nai)
taberu -> tabe(nai)
bi-ru
this seems like a mishearing of #5529
クラス 暮らす
dc
Can you make this a adjective? Like, let's say:
Shinjirarenai hanashi (The story that is not believed)
Could you say:
Shinjirarezu hanashi
Ayumi
信じられず comes up in google with quite a few hits, but this is a verb. "without believing". I think your example might be an adverb - as you are using it to modify another verb?

eg:
幼い頃に母に捨てられ、愛を信じられずに育ったカン・ジェホは、働きながら大学に通う苦学生。
dc