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I heard if you jailbreak you can't access mail or safari ? That is a huge down

Untethered means you can reboot your iphone and turn it off and back on with out any problems and tethered means that you have to boot you iphone with a computer using redsnow start you iphone back up.

There are 3 sorts of jailbreaks ATM. I'll explain these 3 to you.
The 3 jailbreaks are:

• tethered(bad)
  
• semi-tethered(good)
  
• untethered(best)
  

Tethered
When a jailbreak is tethered it means that each time you shut down your phone, it won't be able to reboot without a computer which is quite awfull when you're out of town and have no computer near you. Unless you are a jailbreak hardcore I won't recomend this sort of jailbreak to you.

semi-tethered
The biggest difference with tethered and semi-tethered is that this is also a tethered jailbreak BUT you can reboot your iphone/ipod/ipad without a computer. Though after the reboot you won't be able to use safari and some other apps(obviously cydia won't work either) anymore untill you reboot your iDevice with the computer. But you will be able to make phone calls and send msgs.

Untethered
This isthe best kind of jailbreak you can possibly have! You can reboot your iDevice as much as you like and everything will work, all your jailbreak apps will work, cydia will work, etc... But to have this awesome jailbreak you need to burn 3 exploits so that's why it's taking so long before a untethered jailbreak for ios 6 comes out. If you're still on 5.1 you're lucky because then you can still jailbreak your iphone untethered.

If you have more questions feel free to ask