Bitcoin Core is open source under an MIT license, and is the original software implementation of a Bitcoin full node, though there are others. Most nodes run Bitcoin Core, but don't have to. Bitcoin could be defined as a network of users that agree to the same consensus rules, which means they don't all have to run the same exact software.
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Right; it's like asking if the Internet is open source. Certainly a large portion of the infrastructure that supports the Internet is open source, but there there also less open pieces around. Perhaps a better question is whether you can interact fully with Bitcoin with just open source software, in which case the answer is yes. – Pieter Wuille – 2018-10-15T16:57:24.560
I dunno. Is GCC not "open source" because people sometimes write proprietary software with it? :) – G. Maxwell – 2018-10-15T17:13:42.517
@G Maxwell But "GCC" isn't the name given to the ecosystem of software compiled with GCC. – Pieter Wuille – 2018-10-16T03:33:25.850