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What is an adele?

What is an adele? Here are some definitions.

Noun
  1. (mathematics) A member of a self-dual topological ring built on the field of rational numbers (or, more generally, any algebraic number field), and involving in a symmetric way all the completions of the field.
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Examples
Adele brushes her perfectly manicured fingertips atop the cold, smooth metal of the letter opener.
As everyone spilled out of the studio and into the corridor, Adele pushed her way through and approached Harry Eastman's door.
When Hope and Gabe got home that day, Adele had an idea firmly lodged in her mind.
She scribbled a few things on a yellow legal pad and left to give Adele privacy while she undressed.
Once she had upset Sophie because Sophie was playing with her dolls and making much noise and Adele tried to reprehend her.
Adele turned the faucet on and adjusted the water to a non-scalding temperature.

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