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I bought a new Mac and would like to install previous versions of Mathematica on it. Unfortunately, I lost my USB containing all the .dmg files of previous versions of Mathematica for Mac OS. But, I still have them all installed on my older mac in the standard Applications directory. Is it possible to use these installed version to somehow recreate the dmg files, so that I may install them on my new computer? If so, how?

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You do not need to recreate any DMG files. The DMG files are simply a means to store Mathematica.app, just like a zip file. You can simply zip up (compress) Mathematica.app on your old computer, transfer to the new one, then uncompress. This assumes that you made no modifications to Mathematica's $InstallationDirectory on your old computer (i.e. you did not right-click Mathematica.app, choose Show Package Contents, then modify the contents).

This works because most Mac apps do not need any installation at all. Applications are usually self-contained, and can be copied around freely.

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