All game cartridges contain a copy of the required system version to play it, allowing anyone on a lower version to use the cartridge to update to that version (even without an internet connection).
Note that cartridge updates will only deliver updates to core features, such as the System Settings, Home Menu, etc. cartridge updates will not deliver updates to Nintendo 3DS Sound and Network features, such as System Transfer, Internet Browser, StreetPass Mii Plaza, or eShop.
This means that using a cartridge update from a version containing an older Nintendo 3DS Sound version *(<3.0.0)* to one that introduced a newer Nintendo 3DS Sound version will break [Soundhax](homebrew-launcher-(soundhax))! You will need an [alternate method](homebrew-launcher-(alternatives)) of entering the Homebrew Launcher!
This also means that a cartridge update will NOT install a browser if you do not already have one. This will **only** update the actual system version *(for example, 2.1.0-0 -> 6.0.0-0)*. The last number *(the -0)* will **not** change.