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There is nothing wrong with downloading and using your own copy of jQuery, but you do have another option available that can help to improve the performance of your websites. That's to use a CDN-hosted copy of jQuery.
In case you don't know, a CDN is a Content Delivery Network. The premise behind a CDN is that files download faster from the servers that are physically closer to a site visitor's location. So, for example, if you're in Los Angeles, California, a copy of jQuery that's on a server in Phoenix, Arizona will download faster than a copy that's on a server in New York City. To help this along, a CDN has a copy of the same file on lots of different servers all around the world. Each time a site visitor requests a file, the CDN smartly routes their request to the closest available server, helping to improve response times and overall site performance.