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is it generally set in the setting while you wait
and in your full view?
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Generally, no. Jewelers usually work on many pieces at one time, taking each through each phase of the process all at once, and finishing them all together.
To do the entire process on one piece only interrupts the integrated process on all the pieces, and is not the norm.
In addition to this, many jewelers don't like people looking over their shoulders. It makes some of them nervous, while others get agitated because they think their integrity is being questioned. After all, the reason most people are watching is because they want to make sure the jeweler doesn't steal their diamond. The implication of being considered a possible thief is aggravating for some.
In order to get a while-you-wait setting job done, you will have to specifically request it. Some jewelers don't mind doing it all. Many will charge an extra premium for while-you-wait-and-watch service.