Akademik

нет числа
СЧЕТУ <-a> НЕТ кому-чему coll; НЕТ <НЕСТЬ obs> ЧИСЛА{{}}
[VP; impers]
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some people (things etc) are present or exist in very great or infinite numbers:
- Х-ам счёту нет{{}} there are innumerable (countless, myriad) Xs;
- there is no counting (no end to) the Xs;
- there are more Xs than one can count.
     ♦ ...Находившийся перед ним [Чичиковым] узенький дворик весь был наполнен птицами и всякой домашней тварью. Индейкам и курам не было числа... (Гоголь 3). ...The small yard outside was full of birds and all sorts of domestic creatures. There were innumerable chickens and turkey hens... (3e). ...He [Chichikov] saw that the narrow yard was teeming with fowl and every kind of domestic animal. There was no counting the turkeys and hens... (3d).

Большой русско-английский фразеологический словарь. — М.: ACT-ПРЕСС КНИГА. . 2004.