Implied in example sentence

Einstein had thought a little bit more about his theory, and realized it also implied that mass and energy, one apparently solid and the other supposedly ethereal, were actually equivalent.

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Privacy is implied.

In the early 19th century, if you were a geologist and made a claim about the age of the Earth, you had to explain whether that was consistent or how it was or wasn't consistent with the age of the Earth implied by the account in Genesis.

I want the happy ending implied by the title to my article, which is, incidentally, the only part of the article that I didn't actually write.

This implied that everything should have started with the monumental explosion of an infinitely hot, infinitely small point.

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