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This post says

I don't believe there can be such a thing as "non-sequential" ordering, because if any items were listed without a sequence then they would not be any order.

The expression "there can be" sounds uncommon, is this expression "I don't believe non-sequential ordering exists" more idiomatic?

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Both versions are fine, and they are basically equivalent. There's no problem with "there can be," in my opinion.

There may be a very slight difference in meaning. The simple version "I don't believe X exists" seems to accept that X may be well-defined but probably doesn't exist. The "I don't believe such a thing as 'X' exists" means that although someone can say "X," it doesn't have a well-defined meaning, so it doesn't even make sense to talk about whether or not it exists.

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