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There's a doll inside that doll and inside that doll there's a doll and inside that doll there's a doll and it goes on to infinity.

There's a doll inside that doll and inside that doll there's a doll and inside that doll there's a doll and inside that doll there's a doll...

Is the right expression "goes on to infinity". I am not sure if it's idiomatic. I don't want to say etc. or something along that line, I rather use an idiomatic phrase.

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    It would normally be goes on infinitely. (And in the case of a doll, it can only be used metaphorically.) Saying to infinity is normally an expression of a location or destination. – Jason Bassford May 17 at 17:44
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    "...and so on, for ever." As a child I was fascinated by a certain brand of soup can whose label showed a picture of a housewife holding a can of soup, and that can's label showed... In the computer world, this can be called "nesting" or "recursion". – Weather Vane May 17 at 17:54
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    I'd say you've already gone way past "idiomatic" by the time you've repeated the word doll 6 times! In this exact context, you're using that word twice for each level of recursion, so it would probably be best to stop at 4 repetitions (i.e. - 2 levels). But if it weren't for that "twice per level" situation, the default "rule of three" principle (for almost any "list-type" context) would probably be the way to go. – FumbleFingers Reinstate Monica May 17 at 18:04
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    I think the Latin phrase "ad infinitum", "to infinity", is quite idiomatic. "Big bugs have little bugs, Upon their backs to bite 'em, And little bugs have lesser bugs, and so, ad infinitum." – Jack O'Flaherty May 17 at 18:40
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    As some cosmologists say, "it's turtles all the way down". – Michael Harvey May 17 at 19:25

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