When my wireless is turned off, and I get near an open wireless network, it automatically connects to it. (Why?)
How can I completely turn off the Wi-Fi so that my phone will not do such insecure things?
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Another thing that you may want to uncheck is the alerts for open wireless networks and forget all the networks your phone has already connected to, as most Android phones are, by default, set up to re-connect to wireless networks they've already connected to. You can find these options, as Matthew Read said above, under Settings > Wireless and Network.