camel's nose

The root phrase is usually claimed to be a saying of Arabs or Middle Eastern cultures, roughly as follows:

Do not allow a camel to put his nose under the edge of your tent, for soon you will have a camel in your tent.

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camel's nose (plural camels' noses)

1. (idiomatic) A situation where the permitting of some small act will lead to a larger undesirable act or circumstance.

• foot in the door
• give them an inch and they'll take a mile
• slippery slope
• thin edge of the wedge

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