You do not need a wireless network for the PS3. The PS3 can be connected via ethernet cable as well. And is the best way to connect the PS3 to online to prevent the possibility of lag when playing online.
You can also use the PS3 without the Online connection to Play games, DVDs and Blu-Ray Discs, but the online connection does help with updates besides allowing the use of the PlayStation Network, Store and online gaming.
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